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Question
Solve the following :
Find the area of the region bounded by the following curve, the X-axis and the given lines : y = sin x, x = 0, x = π
Solution
The curve y = sin x intersects the X-axis at x = 0 and x = π between x = 0 and x = π.
Two bounded regions A1 and A2 are obtained. Both the regions have equal areas.
∴ required area = A1 + A2 = 2A1
= `2 int_0^(pi/2) y*dx, "where" y = sin x`
= `2int_0^(pi/2) sinx*dx`
= `2[- cos x]_0^(pi/2)`
= `2[- cos pi/2 cos 0]`
= 2(– 0 + 1)
= 2 sq units.
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