Given that m and n are positive integers, show that 10xm(1 x)n dx = 10xn(1 x)m dxby

Chapter 5, Problem 54

(choose chapter or problem)

Given that m and n are positive integers, show that

$\int_{0}^{1} x^{m}(1-x)^{n} d x=\int_{0}^{1} x^{n}(1-x)^{m} d x$

by making a substitution. Do not attempt to evaluate the integrals.

Equation Transcription:

$\int\limits_{0}^{1}\ {\ {x}^{m}{(1-x)}^{n}dx=\int\limits_{0}^{1}\ {x}^{n}{(1-x)}^{m}\ dx\ \ }^{\ }$

Text Transcription:

integral_0^1 x^m(1 − x)^n dx = intergral_0 ^1 x^n(1 − x)^m dx

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