InterviewSolution
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InterviewSolution
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`int_(0)^(sqrt(2))sqrt(2-x^(2))dx=?`A. `pi`B. `2pi`C. `(pi)/(2)`D. none of these |
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Answer» Put `x=sqrt(2)sint` and `dx=sqrt(2)cost dt`. `[x=0impliest=0]` and `[x=sqrt(2)impliest=(pi)/(2)]` `:.I=int_(0)^(pi//2)sqrt(2-2sin^(2)t)*sqrt(2)costdt=2int_(0)^(pi//2)cos^(2)tdt=2int_(0)^(pi//2)(1)/(2)(1+cos2t)dt` `=[t+(sin2t)/(2)]_(0)^(pi//2)=(pi)/(2)`. |
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