First slide

Evaluation of definite integrals

Question

The value of $\int_{0}^{π^{2} / 4} \sin \sqrt{x} d x$ is

Easy

A

0
B

1
C

2
D

none of these

Solution

Putting $\sqrt{x} = t$ $d x = 2 t d t$
$\begin{array}{l} \int_{0}^{π^{2} / 4} \sin \sqrt{x} d x = 2 \int_{0}^{π / 2} t \sin t d t \\ = 2 [- t \cos t]_{0}^{π / 2} + \int_{0}^{π / 2} \cos t d t] \\ = 2 [0 + {\sin t|}^{π / 2}_{0}] = 2 \end{array}$

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