First slide

Evaluation of definite integrals

Question

$\int_{0}^{π^{2} / 4} \cos \sqrt{x} d x$

Moderate

A

$π - 2$
B

$π + 2$
C

$\frac{π}{2} - 1$
D

2

Solution

$\begin{array}{l} Put \sqrt{x} = t \Rightarrow x = t^{2} \Rightarrow d x = 2 t d t \\ \int_{0}^{π^{2} / 4} \cos \sqrt{x} d x = \int_{0}^{π / 2} (\cos t) \cdot 2 t d t LL⇒ t = 0, U . L t = \sqrt{\frac{π^{2}}{4} \Rightarrow} t = \frac{π}{2} \end{array} = {(2 t \sin t)}^{\frac{π}{2}}_{0} - \int_{0}^{\frac{π}{2}} 2 \sin t d t = π - 2$

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