InterviewSolution
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InterviewSolution
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`int(sqrtx)/(sqrt(a^(3)-x^(3)))dx` equal toA. `(1)/(3)sin^(-1)sqrt((x^(3))/(a^(3)))+C`B. `(2)/(3)sin^(-1)sqrt((x^(3))/(a^(3)))+C`C. `(2)/(3)sin^(-1)sqrt((x)/(a))+C`D. None of these |
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Answer» Correct Answer - B We have, `l=int(sqrtx)/(sqrt(a^(3)-x^(3)))dx` `l=int(sqrtx)/(sqrt((a^(3//2))^(2)-(x^((3)/(2)))^(2)))dx` Put`" "x^((3)/(2))=t` `rArr" "(3)/(2)x^((1)/(2))dx=dt" "rArr" "sqrtxdx=(2)/(3)dt` `therefore" "l=(2)/(3)int(dt)/(sqrt((a^((3)/(2)))^(2)-t^(2)))=(2)/(3)sin^(-1)((t)/(a^((3)/(2))))+C` `=(2)/(3)sin^(-1)((x^((3)/(2)))/(a^((3)/(2))))+C=(2)/(3)sin^(-1)sqrt((x^(3))/(a^(3)))+C` |
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