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Area between the curve $y=\cos x$ and $x$ - axis when $0 \leq x$ is
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Verified Answer
The correct answer is:
$4$
$\begin{array}{l}y=\cos x \text {, When } x \in\left[0, \frac{\pi}{2}\right], \cos x \geq 0 \\\text { When } x \in\left[\frac{\pi}{2}, \frac{3 \pi}{2}\right], \cos x \leq 0 \\\text { When } x \in\left[\frac{3 \pi}{2}, 2 \pi\right], \cos x \geq 0\end{array}$
Thus required area is given by,
$\begin{aligned}\int_0^{\pi / 2} y d x & =\int_0^{\pi / 2} \cos x d x+\int_{\pi / 2}^{3 \pi / 2}(-\cos x) d x+\int_{3 \pi / 2}^{2 \pi} \cos x d x \\& =1+2+1=4 \text { sq. unit. }\end{aligned}$
Thus required area is given by,
$\begin{aligned}\int_0^{\pi / 2} y d x & =\int_0^{\pi / 2} \cos x d x+\int_{\pi / 2}^{3 \pi / 2}(-\cos x) d x+\int_{3 \pi / 2}^{2 \pi} \cos x d x \\& =1+2+1=4 \text { sq. unit. }\end{aligned}$
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