First slide

Evaluation of definite integrals

Question

$\int_{0}^{1} \frac{4 x^{3}}{\sqrt{1 - x^{8}}} d x =$

Easy

A

$\frac{π}{4}$
B

$\frac{π}{2}$
C

$π$
D

$\frac{π}{8}$

Solution

$\int_{0}^{1} \frac{4 x^{3}}{\sqrt{1 - {(x^{4})}^{2}}} d x = {[S i n^{- 1} (x^{4})]}_{0}^{1} = \frac{π}{2}$

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