InterviewSolution
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InterviewSolution
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` int _(0)^(pi//2) x sin^(2) x cos^(2) x dx ` is equal toA. `(pi^(2))/(32)`B. `(pi^(2))/(16)`C. `(pi)/(32)`D. None of these |
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Answer» Correct Answer - D Let ` l = int _(0)^(pi//2) x sin^(2) x cos ^(2) x dx " "` …(i) ` rArr l = int _(0)^(pi//2)(pi/2-x) x sin^(2) x cos^(2) x dx " "` …(ii) On adding Eqs . (i) and (ii) , we get ` 2l = pi/2 int_(0)^(pi//2) sin^(2) x cos ^(2) x dx ` ` = pi/8 int _(0)^(pi//2) sin^(2) 2 x dx = pi/8 int _(0)^(pi//2) ((1-cos 4x)/2) dx` ` rArr 2l = pi/16 [ x - (sin 4x)/4]_(0)^(pi//2)` ` rArr 2l = pi/16 [ pi/2]` ` rArr l = (pi^(2))/64` |
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