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Integration by Substitution: Definite Integrals

Calculus: We note how integration by substitution works with definite integrals using the First Fundamental Theorem of Calculus. Two methods are given, and examples used are (a) int_0^1 x(x^2+1)^5 dx, (b) int_0^{pi/4} tan(x) sec^2(x) dx, (c) int_{-1}^1 x(1-x^2)^2 dx, and (d) int_0^2 x(1-x^2)^2 dx.
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