187 Integral 1

Calculus Level 2

What is the value of $\int^{1}_{-1}\left(\frac{\sin^{-1}{x}}{\sqrt{2-x^{12}}}+|x|\right)\,dx?$

\frac{2\pi}{9}

\frac{2\pi}{9}+1

\frac{\pi}{9}+\frac{1}{2}

1 solution

Leslie C
Sep 29, 2020

$\frac{\sin^{-1}{x}}{\sqrt{2}-x^{12}}$ is an odd function, thus, the interval $[-1,1]$ is symmetric about 0. This means the first part of the integral is 0.

Now, since $|x|$ is even, $\int^{1}_{-1}|x|\,dx=2\int^{1}_{0}x\,dx=1$

187 Integral 1

1 solution

0 pending reports