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Area between x=g(y) and y Axis

Find the area...

Question

Find the area of the region enclosed by the curves;
$y = cos x$ , $y = 1 - \frac{2 x}{π}$

A

2 - \frac{π}{2}

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B

π

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C

\frac{π}{2}

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D

1

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Solution

The correct option is B $2 - \frac{π}{2}$
$y = 1 - \frac{2 x}{π}$ , $y = cos x$
$A = (0, 1)$ , $B = (\frac{π}{2})$
Area of shaded region above X-axis
$= \int_{0}^{\frac{π}{2}} cos x d x - \frac{1}{2} \times \frac{π}{2} \times 1$
$= [sin x]_{0}^{\frac{π}{2}} - \frac{π}{4}$
$= 1 - \frac{π}{4}$
Due to symmetry
Total area $= 2 - \frac{π}{2}$

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