First slide

Evaluation of definite integrals

Question

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

Easy

A

$\frac{π}{8}$
B

$\frac{3 π}{8}$
C

$\frac{5 π}{4}$
D

$\frac{π}{2}$

Solution

$\int_{0}^{1} \sqrt{x (1 - x)} d x = \frac{π}{8} {(b - a)}^{2} = \frac{π}{8} {(1 - 0)}^{2} = \frac{π}{8}$

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