InterviewSolution
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InterviewSolution
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` int _(-3pi//2)^(-pi//2) [ ( x + pi)^(3) + cos^(2) x ] ` dx is equalt toA. `((pi^(4))/32)+(pi/2)`B. ` (pi/2)`C. ` (pi/4)-1`D. ` (pi^(4))/32` |
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Answer» Correct Answer - B Let ` l = int_(-3pi//2)^(-pi//2)[(x+pi)^(3)+cos^(2)x]dx` … (i) `rArrl = int_(-3pi//2)^(-pi//2)` `[(-(pi)/(2)-(3pi)/(2)-x+pi)^(3)+cos^(2)(-(pi)/(2)-(3pi)/(2)-x)]dx` `rArr l = int_(-3pi//2)^(-pi//2)[-(x+pi)^(3)+cos^(2)x]dx` … (ii) On adding Eqs . (i) and (ii) , we get `2l=int_(-3pi//2)^(-pi//2)2cos^(2)x dx=int_(-3pi//2)^(-pi//2)(1+cos2x)dx` `=[x+(sin2x)/(2)]_(-3pi//2)^(-pi//2)` `=[-(pi)/(2)+(sin(-pi))/(2)-(-3pi)/(2)+(sin(-3pi))/(2)]` `rArrl=(pi)/(2)` |
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