Q. 175.0( 1 Vote )

Find the area bounded by the curve y = sinx between x = 0 and x = 2π

Answer :

Plot the graph of sinx from 0 to 2π and the required area is shaded



Now observe that the area from 0 to π is above X-axis and the area from π to 2π is below X-axis


The area below X-axis will be negative


Also the areas under sinx from 0 to π and π to 2π are equal in magnitude but they will have opposite sign


Hence if we integrate sinx from 0 to 2π the two areas will cancel out each other as they have opposite signs and we will end up on 0


So either find area under sinx from 0 to π and multiply it by 2 or split the limit 0 to 2π into 0 to π and π to 2π


Here we will split the limit


y = sinx


Integrating from 0 to 2π




Because where c (a, b)


Here π (0, 2π)


Also now observe that when x is from π to 2π sinx is negative


Hence for π to 2π sinx will become -sinx








Hence area bounded by sinx from 0 to 2π is 4 unit2


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