First slide

Area of bounded Regions

Question

$Area bounded by the curves$ $y = \sin x and y = \cos x between two consecutive points of the$ $intersection.$

Difficult

A

1
B

2
C

3
D

4

Solution

$Two consecutive points of intersection of y = \sin x and y = \cos x can be taken as x = π / 4 and x = 5 π / 4 . Therefore,$
$\begin{aligned} Required area = \int_{π / 4}^{5 π / 4} (\sin x - \cos x) d x \\ = [- \cos x - \sin x]_{π / 4}^{5 π / 4} \\ = \frac{2}{\sqrt{2}} + \frac{2}{\sqrt{2}} = 2 \sqrt{2} sq. units \end{aligned}$

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