Integration by substitution
If the function u = g(x) has a continuous derivative on [a, b] and f is continuous on the range of g, then
Steps for Integrating by Substitution—Definite Integrals 1. Choose a substitution u = g(x), such as the inner part of a composite function. 2. Compute 3. Re-write the integral in terms of u and du, with the u-limits of integration. 4. Find the resulting integral in terms of u. 5. Evaluate using the u-limits. No need to switch back to x’s!
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. Compute new u-limits of integration g(a) and g(b).
