Compute integrals of combinations of powers, sines, cosines, exponentials and logarithms that are solvable by substitution by hand.Īn interactive script that presents visualizations of integration by parts as well as focused and randomized practice with immediate feedback. Explain what the method of substitution is and how it works.Compute integrals of linear combinations of powers, sines, cosines, and exponentials by hand.Īn interactive script that presents visualizations of u-substitution and integration by parts as well as scaffolded and randomized practice with immediate feedback.Explain and apply the trapezoidal approximation.Īn interactive script that facilitates exploration of the results of applying the integral as an antiderivative and presents opportunities for practice with immediate feedback.Discuss the implications for applying calculus in applications with values that are discrete or continuous.Explain and apply the different approximations computed by a left-endpoint, right-endpoint, midpoint, maximum, or minimum method of selecting a height value in a Riemann sum.This script includes an analysis of real power generation data as well as visualizations of the error in each approximation method. This folder includes scripts that integrate visualizations with instructional content and practice for active instruction or supported review.Īn interactive script that facilitates exploration of simple geometric integral approximations including both rectangular and trapezoidal approximation methods. Looking for more? Find an issue? Have a suggestion? Have questions?Ĭontact the MathWorks online teaching team. MATLAB Onramp – a free two-hour introductory tutorial that teaches the essentials of MATLAB. If you wish a more complete introduction to MATLAB, you can take Minimal use of MATLAB syntax is required to complete some of the interactive practice, but it is all reviewed in the scripts themselves as needed. With the exception of integralRiemann.mlx and vizRiemann.mlx, the scripts are written to follow Calculus-Derivatives and expect basic understanding of derivatives and derivative rules. It also assumes knowledge of basic area formulas, including the area of a trapezoid. This module assumes a knowledge of functions that is standard in precalculus course materials regarding powers, exponentials, absolute values, logarithms, sines, cosines, rational functions, and asymptotes. To stop running the script or a section midway (for example, when an animation is in progress), use the Stop button in the RUN section of the Live Editor tab in the MATLAB Toolstrip. Get started with each live script by running it one section at a time. The instructions inside the live scripts will guide you through the exercises and activities. Opening Integrals.prj will add the module to your MATLAB path and open a navigation page where you can choose interactive examples by topic or type. The module is divided into three folders with the same content offered for different use: Full Scripts, Visualizations, and Practice. These live scripts can be used as part of a lecture, as activities in an instructional setting, or as interactive assignments to be completed outside of class. It also covers the indefinite integrals of powers, exponentials, natural logarithms, sines and cosines as well as substitution and integration by parts. There is a focus on numerical approximation and graphical representation as tools for understanding the concepts of integral calculus.Ĭalculus-Integrals covers Riemann sum approximations to definite integrals, indefinite integrals as antiderivatives, and the fundamental theorem of calculus. This curriculum module contains interactive live scripts and a MATLAB® app that teach basic concepts of integral calculus. Compatible with R2021b and later releases.
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