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Find the area of the region bounded ...

Find the area of the region bounded by the curve ` y = sinx `, the lines ` x = - ( pi ) /(2), x = ( pi ) /(2) ` and X- axis.

Text Solution

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Required area = area of the shaded region
` = 2` ( area of the region OBNO )
` = 2 int _ ( 0 ) ^ ( pi//2) ydx ` , where ` y =sinx `
` = 2 int _ 0 ^(pi//2) sin x dx `
` = 2 [ - cos x ] _ 0 ^((pi)/(2)) `
` = 2 [ - cos ""(pi)/(2) + cos 0] `
` 2 [ - 0 + 1 ] = 2 ` sq units.
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