The area between X -axis and the curve y = cos x when 0 x 2 is:

Question

The area between $X$ -axis and the curve $y = \cos x$ when $0 \leq x \leq 2 π$ is:

Smart Achievers · Accepted Answer

(4)

Ans. 4 sq. unit

Explanation:

$y = \cos x,$ $0 \leq x \leq 2 π$

$\cos x \geq 0 when x \in [0, \frac{π}{2}]$

$\cos x \leq 0 when x \in [\frac{π}{2}, \frac{3 π}{2}]$

$\cos x \geq 0 when x \in [\frac{3 π}{2}, 2 π]$

$∴$ $Area = \int_{0}^{π / 2} \cos x d x + \int_{π / 2}^{3 π / 2} \cos x d x + \int_{3 π / 2}^{2 π} \cos x d x$

$= 1 + 2 + 1$

$= 4 sq. units$

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