InterviewSolution
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InterviewSolution
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`int_(0)^(pi) x sin^(2) xdx` का मान ज्ञात कीजिएः |
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Answer» `int x. sin^(2) xdx =1/ int x(1-cos 2x)dx` `=1/2 int (x-xcos 2x)dx` `=1/4x^(2)-1/2int x cos 2 xdx` `=1/4x^(2)-1/2 [(x sin 2x)/(2)-int (1. sin 2x)/(2)dx]` `=1/4x^(2)-1/4x sin 2x-1/8 cos 2x` `therefore underset(0)overset(pi)int x.sin^(2)xdx=1/4 [x^(2)-x sin 2x-1/2 cos 2x]_(0)^(pi)` `=1/4 [pi^(2)-pisin 2pi-1/2 cos 2pi-0+0.sin 0+1/2 cos 0]` `=1/4[pi-0+1/2+1/2]=(pi^(2))/(4)` |
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