Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 4 - Integration - 4.9 Evaluating Definite Integrals By Substitution - Exercises Set 4.9 - Page 341: 38

Answer

See explanation.

Work Step by Step

Let $d u=-d x$ and $-x+1=u$ Simplify $\int_{0}^{1} x^{m}(-x+1)^{n} d x=-\int_{1}^{0}(-u+1)^{m} u^{n} d u$ Rewrite integral $\int_{0}^{1} x^{m}(-x+1)^{n} d x=\int_{0}^{1}(-u+1)^{m} u^{n} d u$ Replace X with U, du with dx $\int_{0}^{1}(-x+1)^{m} x^{n} d x=\int_{0}^{1} x^{m}(-x+1)^{n} d x$
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