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Explore the concept of antiderivatives and indefinite integration, learn how to find equations, solve initial value problems, and understand differential equations. This comprehensive guide covers basic integration rules, exercises, and techniques for rewriting, integrating, and simplifying.
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4.1 : Anti-derivatives Greg Kelly, Hanford High School, Richland, Washington
Consider: or then: Given: find First, a little review: It doesn’t matter whether the constant was 3 or -5, since when we take the derivative the constant disappears. However, when we try to reverse the operation: We don’t know what the constant is, so we put “C” in the answer to remind us that there might have been a constant.
Given: and when , find the equation for . This is called an initial value problem. We need the initial values to find the constant. An equation containing a derivative is called a differential equation. It becomes an initial value problem when you are given the initial condition and asked to find the original equation. If we have some more information we can find C.
Front Cover #15? 4.1 Antiderivatives and Indefinite Integration
Basic Integration Rules These two equations allow you to obtain integration formulas directly from differentiation formulas, as shown in the following summary.
Basic Integration Rules cont’d
Practice Exercises OriginalRewriteIntegrateSimplify
