1.

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»

Solution :
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.


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