integral two question

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1. Given a constant a>0 , show that $\int_{a}^{-a} f(x)dx=\int_{0}^{a} [f(-x)+f(x)]dx .....and hence, evaluate \int_{-1}^{1} ln(x+\sqrt{1+x^2})dx$

2.Prove or disprove : If f is continuous , then $\int_{0}^{1} f(x) dx=\int_{0}^{1} f(1-x)dx$

Guest Apr 11, 2016

ElectricPavlov · Answer 1 · 2016-04-11T12:42:10

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1/2x^2 = 1/2 (1^) = 1/2 x-1/2x^2 = 1- 1/2(1^2) = 1/2

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