InterviewSolution
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InterviewSolution
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`int_(0)^(pi//2) x^(2) cos xdx` का मान ज्ञात कीजिएः| |
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Answer» `underset(0)overset(pi//2)int underset(I)(x^(2)) underset(II)(cos) xdx` `=x^2underset(0)overset(pi//2)int cosdx-int [d/dxx^(2)int cos x]dx` `=x^(2) sin x-iint [2x.sin x]dx` `=x^(2) sin x-2[x.int sin xdx-int {d/dxx int sin xdx }dx` `=x^(2) sin x-2[x.(-cos x)-int 1(-cos x)dx]` `=x^(2)sin x+2x cos x-2int cos xdx` `=x^(2)sinx+2x cos x-2 sin x` `=x^(2) sin x+2x cos x -2 sin x` `=(x^(2)-2)sin x+2x. cos x` `therefore underset(0)overset(pi//2)int x^(2)cosxdx` `=[(x^(2)-2)sin x+2x. cosx]_(0)^(pi//2)` `=[((pi^(2))/(4)-2).sin""pi/2+2xxpi/2xxcos""pi/2]-[(0-2)sin 0+2(0) cos 0]` `=[((pi^(2))/(4)-2).1+pi/(0)]=[0+0]` `=(pi^2)/(4)-2` |
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