Question

Find the area bounded by the following curve :
(i) `f(x) = sinx, g(x) = sin^(2)x, 0 le x le 2pi`
(ii) `f(x) = sinx, g(x) = sin^(4)x, 0 le x le 2pi`

Answer 1

As shown in the figure, the area bounded by `y = sin x` and `y = sin^(2)x` is equal to twice the area bounded by y = sin x and the x - axis for `x in [0, pi].` Now we know that the area bounded by y = sin x and the x axis for `x in [0, pi]` is `overset(pi)underset(0)int sin x" " dx = 2 " sq. units"`
Hence the required area is 4 sq. units.