InterviewSolution
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InterviewSolution
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Evaluate: `int_(-a)^a sqrt((a-x)/(a+x)) dx `A. `api`B. `(api)/(2)`C. `2api`D. none of these |
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Answer» Put `x=acostheta` and `dx=-asintheta d theta`. `[x=-aimpliestheta=pi]` and `[x=aimpliestheta=0]`. `:.I=int_(pi)^(0)sqrt((1-costheta)/(1+costheta))*(-asintheta)d theta=aint_(0)^(pi){(2sin^(2)(theta//2))/(2cos^(2)(theta//2))}^(1//2)2sin((theta)/(2))cos((theta)/(2))d theta` `=aint_(0)^(pi)2sin^(2).(theta)/(2)d theta=a int_(0)^(pi)(1-costheta)d theta=api`. |
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