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@@ -19,7 +19,7 @@ This curriculum module contains interactive [MATLAB® live scripts](https://www.
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You can use these live scripts as [demonstrations](#H_9AAE657C) in lectures, class activities, or interactive assignments outside of class. Calculus \- Integrals covers Riemann sum approximations to definite integrals, indefinite integrals as antiderivatives, and the fundamental theorem of calculus. It also covers the indefinite integrals of powers, exponentials, natural logarithms, sines, and cosines as well as substitution and integration by parts. Applications include area and power. In addition to the full scripts, visualizations, and practice scripts there is a [Calculus Flashcards app](#H_1F9459BC) included as well.
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The instructions inside the live scripts will guide you through the exercises and activities. Get started with each live script by running it one section at a time. To stop running the script or a section midway (for example, when an animation is in progress), use the <imgsrc="READMEtest_media/image_0.png"width="19"alt="image_0.png"> Stop button in the **RUN** section of the **Live Editor** tab in the MATLAB Toolstrip.
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The instructions inside the live scripts will guide you through the exercises and activities. Get started with each live script by running it one section at a time. To stop running the script or a section midway (for example, when an animation is in progress), use the <imgsrc="Images/EndIcon.png"width="19"alt="End icon"> Stop button in the **RUN** section of the **Live Editor** tab in the MATLAB Toolstrip.
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Looking for more? Find an issue? Have a suggestion? Please contact the [MathWorks online teaching team](mailto:%20onlineteaching@mathworks.com).
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### Accessing the Module
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### **On MATLAB Online:**
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Use the [<imgsrc="Images/OpenInMO.png"width="136"alt="image_1.png">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj) link to download the module. You will be prompted to log in or create a MathWorks account. The project will be loaded, and you will see an app with several navigation options to get you started.
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Use the [<imgsrc="Images/OpenInMO.png"width="136"alt="Open in MATLAB Online">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj) link to download the module. You will be prompted to log in or create a MathWorks account. The project will be loaded, and you will see an app with several navigation options to get you started.
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### **On Desktop:**
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Download or clone this repository. Open MATLAB, navigate to the folder containing these scripts and double\-click on [Integrals.prj](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj). It will add the appropriate files to your MATLAB path and open an app that asks you where you would like to start.
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Ensure you have all the required products ([listed below](#H_E850B4FF)) installed. If you need to include a product, add it using the Add\-On Explorer. To install an add\-on, go to the **Home** tab and select <imgsrc="Images/AddOnsIcon.png"width="16"alt="image_2.png"> **Add-Ons** > **Get Add-Ons**.
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Ensure you have all the required products ([listed below](#H_E850B4FF)) installed. If you need to include a product, add it using the Add\-On Explorer. To install an add\-on, go to the **Home** tab and select <imgsrc="Images/AddOnsIcon.png"width="16"alt="Add Ons icon"> **Add-Ons** > **Get Add-Ons**.
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<aname="H_E850B4FF"></a>
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# Scripts
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|**Full Script** <br> |**Visualizations** <br> |**Learning Goals** <br> In this script, students will... <br> |**Practice** <br> |
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| :-- | :-- | :-- | :-- |
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|[Antiderivatives.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Antiderivatives.mlx) <br> <imgsrc="Images/adf.png"width="135"alt="image_3.png"> <br> |[Visualizing Antiderivatives](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/AntiderivativesViz.mlx) <br> <imgsrc="Images/family.gif"width="135"alt="image_4.gif"> <br> | $\bullet$ see a graphical presentation of the concept of general antiderivatives. <br> $\bullet$ develop computational fluency with the antiderivatives of powers, <br> sines, cosines, and exponentials. <br> |[Calculate Antiderivatives](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/AntiderivativesPractice.mlx) <br> $\displaystyle {\int \sin (3z)\;dz=-\frac{\cos (3z)}{3}+C}$ <br> |
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| [FundamentalTheorem.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheorem.mlx) <br> <img src="Images/Ski-Area.png" width="135" alt="image_5.png"> <br> | [Visualizing the FTC](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheoremViz.mlx) <br> <img src="Images/FTC-generated.png" width="135" alt="image_6.png"> <br> | $\bullet$ explain the fundamental theorem of calculus. <br> $\bullet$ see why the Fundamental Theorem of Calculus makes sense graphically. <br> $\bullet$ develop computational fluency for definite integrals involving linear and <br>rational combinations of powers, sines, cosines, exponentials and natural <br>logarithms. <br> | [Apply the Fundamental Theorem of Calculus](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheoremPractice.mlx) <br> $\displaystyle {\int_1^3 \frac{1}{w^2 }\;dw=-\frac{1}{3}+1=\frac{2}{3}}$ <br> |
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|[Riemann.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Riemann.mlx) <br> <imgsrc="Images/animSolar.gif"width="135"alt="image_7.gif"> <br> |[Visualizing Riemann Sums](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/RiemannViz.mlx) <br> <imgsrc="Images/AreaUnderCurve.png"width="135"alt="image_8.png"> <br> | $\bullet$ explain and apply the different approximations computed by a <br>left\-endpoint, right\-endpoint, midpoint, maximum, or minimum <br>method of selecting a height value in a Riemann sum. <br> | $\bullet$ explain and apply the trapezoidal approximation. <br> $\bullet$ explain why increasing the number of intervals in an approximation will decrease the error. <br> $\bullet$ discuss the implications for applying calculus in applications with values that are discrete or continuous. <br> |
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| [Substitution.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Substitution.mlx) <br> <img src="Images/SubstIm.png" width="135" alt="image_9.png"> <br> | [Visualizing Substitution](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/SubstitutionViz.mlx) <br> <img src="Images/animSubst.gif" width="135" alt="image_10.gif"> <br> | $\bullet$ explain what the method of substitution is and how it works. <br> $\bullet$ develop fluency with computing integrals of combinations of <br>powers, sines, cosines, exponentials and logarithms that are solvable <br>by substitution by hand. <br> $\bullet$ see a graphical understanding of the method of substitution. <br> | [Apply the method of substitution](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/SubstitutionPractice.mlx) <br> $\displaystyle {\int \frac{\cos \left(\ln (t)+1\right)}{t}\;dt=\sin \left(\ln (t)+1\right)+C}$ <br> |
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| [ByParts.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByParts.mlx) <br> <img src="Images/IBP.png" width="135" alt="image_11.png"> <br> | [Visualizing Integration by Parts](.Scripts/ByPartsViz.mlx) <br> <img src="Images/ibp-generated.png" width="135" alt="image_12.png"> <br> | $\bullet$ explain what the method of integration by parts is and how it works. <br> $\bullet$ develop fluency with computing integrals involving powers, sines,<br> cosines, exponentials and logarithms that are solvable by integration by <br>parts by hand. <br> $\bullet$ see a graphical understanding of the integration by parts formula. <br> | [Apply the method of integration by parts](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByPartsPractice.mlx) <br> $\displaystyle {\int y^2 e^y \;dy=y^2 e^y -2ye^y +2e^y +C}$ <br> $\displaystyle =(y^2 -2y+2)e^y +C$ <br> |
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|[Antiderivatives.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Antiderivatives.mlx) <br> <imgsrc="Images/adf.png"width="135"alt="Family of antiderivatives"> <br> |[Visualizing Antiderivatives](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/AntiderivativesViz.mlx) <br> <imgsrc="Images/family.gif"width="135"alt="Animated family of antiderivatives"> <br> | $\bullet$ see a graphical presentation of the concept of general antiderivatives. <br> $\bullet$ develop computational fluency with the antiderivatives of powers, <br> sines, cosines, and exponentials. <br> |[Calculate Antiderivatives](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/AntiderivativesPractice.mlx) <br> $\displaystyle {\int \sin (3z)\;dz=-\frac{\cos (3z)}{3}+C}$ <br> |
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| [FundamentalTheorem.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheorem.mlx) <br> <img src="Images/Ski-Area.png" width="135" alt="Distance traveled by skier"> <br> | [Visualizing the FTC](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheoremViz.mlx) <br> <img src="Images/FTC-generated.png" width="135" alt="Signed area under a curve"> <br> | $\bullet$ explain the fundamental theorem of calculus. <br> $\bullet$ see why the Fundamental Theorem of Calculus makes sense graphically. <br> $\bullet$ develop computational fluency for definite integrals involving linear and <br>rational combinations of powers, sines, cosines, exponentials and natural <br>logarithms. <br> | [Apply the Fundamental Theorem of Calculus](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/FundamentalTheoremPractice.mlx) <br> $\displaystyle {\int_1^3 \frac{1}{w^2 }\;dw=-\frac{1}{3}+1=\frac{2}{3}}$ <br> |
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| [Riemann.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Riemann.mlx) <br> <img src="Images/animSolar.gif" width="135" alt="Better approximation with smaller rectangles"> <br> | [Visualizing Riemann Sums](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/RiemannViz.mlx) <br> <img src="Images/AreaUnderCurve.png" width="135" alt="Approximation by rectangles"> <br> | $\bullet$ explain and apply the different approximations computed by a <br>left\-endpoint, right\-endpoint, midpoint, maximum, or minimum <br>method of selecting a height value in a Riemann sum. <br> | $\bullet$ explain and apply the trapezoidal approximation. <br> $\bullet$ explain why increasing the number of intervals in an approximation will decrease the error. <br> $\bullet$ discuss the implications for applying calculus in applications with values that are discrete or continuous. <br> |
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| [Substitution.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/Substitution.mlx) <br> <img src="Images/SubstIm.png" width="135" alt="f(flower)"> <br> | [Visualizing Substitution](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/SubstitutionViz.mlx) <br> <img src="Images/animSubst.gif" width="135" alt="Animation of dx and du"> <br> | $\bullet$ explain what the method of substitution is and how it works. <br> $\bullet$ develop fluency with computing integrals of combinations of <br>powers, sines, cosines, exponentials and logarithms that are solvable <br>by substitution by hand. <br> $\bullet$ see a graphical understanding of the method of substitution. <br> | [Apply the method of substitution](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/SubstitutionPractice.mlx) <br> $\displaystyle {\int \frac{\cos \left(\ln (t)+1\right)}{t}\;dt=\sin \left(\ln (t)+1\right)+C}$ <br> |
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| [ByParts.mlx](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByParts.mlx) <br> <img src="Images/IBP.png" width="135" alt="Geometric integration by parts"> <br> | [Visualizing Integration by Parts](.Scripts/ByPartsViz.mlx) <br> <img src="Images/ibp-generated.png" width="135" alt="Integration horizontally and vertically"> <br> | $\bullet$ explain what the method of integration by parts is and how it works. <br> $\bullet$ develop fluency with computing integrals involving powers, sines,<br> cosines, exponentials and logarithms that are solvable by integration by <br>parts by hand. <br> $\bullet$ see a graphical understanding of the integration by parts formula. <br> | [Apply the method of integration by parts](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Scripts/ByPartsPractice.mlx) <br> $\displaystyle {\int y^2 e^y \;dy=y^2 e^y -2ye^y +2e^y +C}$ <br> $\displaystyle =(y^2 -2y+2)e^y +C$ <br> |
1.[<imgsrc="Images/OpenInMO.png"width="136"alt="Open in MATLAB Online badge">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals&project=Integrals.prj&file=Apps/CalculusFlashcards.mlapp)
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<aname="H_F61733D7"></a>
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# License
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| <br>[**Numerical Methods with Applications**](https://www.mathworks.com/matlabcentral/fileexchange/111490-numerical-methods-with-applications) <br> | <imgsrc="Images/AreaLake.png"width="171"alt="image_20.png"> <br> |[<imgsrc="Images/OpenInFX.png"width="91"alt="image_21.png">](https://www.mathworks.com/matlabcentral/fileexchange/111490-numerical-methods-with-applications) <br> [<imgsrc="Images/OpenInMO.png"width="136"alt="Open in MATLAB Online badge">](https://matlab.mathworks.com/open/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications/project=NumericalMethods.prj) <br>[GitHub](https://github.com/MathWorks-Teaching-Resources/Calculus-Derivatives) <br> |
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Or feel free to explore our other [modular courseware content](https://www.mathworks.com/matlabcentral/fileexchange/?q=tag%3A%22courseware+module%22&sort=downloads_desc_30d).
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