Integration by substitution - Updated
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This document discusses integration by substitution, which is a technique for evaluating indefinite integrals. It explains the basic substitution formula f'(g(x))g'(x)dx = f(g(x))+C and covers recognizing when substitution can be used with polynomials and trigonometric functions. The document provides 8 examples of using integration by substitution to evaluate definite and indefinite integrals. Videos are referenced for additional explanation and demonstration of each step of the integration by substitution process.
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Integration by substitution - Updated
- 1. AP Calculus Integration by Substitution
- 2. 𝑓′(𝑔 𝑥 ) 𝑔′ 𝑥 𝑑𝑥 = 𝑓(𝑔 𝑥 ) + 𝐶 Integration by Substitution Part I Recognizing the Form With polynomials and trigonometric functions With indefinite and definite integrals
- 3. Examples 1. Find 𝑥2 + 1 2 2𝑥 𝑑𝑥 2. Find 5cos(5𝑥)𝑑𝑥 3. Find 𝑥 𝑥2 + 1 2 𝑑𝑥 4. Find 2𝑥 − 1𝑑𝑥 5. Find 𝑥 2𝑥 − 1𝑑𝑥 6. Find sin2 3𝑥 cos 3𝑥 𝑑𝑥 7. Find 0 1 𝑥 𝑥2 + 1 3 𝑑𝑥 8. Find 1 5 𝑥 2𝑥−1 𝑑𝑥
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