InterviewSolution
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InterviewSolution
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The value of the integral `intx sin^(-1)xdx` is equal toA. `(1)/(2)x^(2)sin^(-1)x+(1)/(4)xsqrt(1-x^(2))-(1)/(4)sin^(-1)x+C`B. `(1)/(2)x^(2)sin^(-1)x-(1)/(4)xsqrt(1-x^(2))-(1)/(4)sin^(-1)x+C`C. `(1)/(2)x^(2)sin^(-1)x+(1)/(4)xsqrt(1-x^(2))+(1)/(4)sin^(-1)x+C`D. `(1)/(2)x^(2)sin^(-1)x+(1)/(4)sqrt(1-x^(2))-(1)/(4)sin^(-1)x+C` |
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Answer» Correct Answer - A Let `l=int x sin^(-1)xdx` On using integration by parts, we get `l=(sin^(-1)x)(x^(2))/(2)-int(1)/(sqrt(1-x^(2))).(x^(2))/(2)dx` `rArr" "l=(x^(2))/(2)sin^(-1)x+(1)/(2)int(-x^(2))/(sqrt(1-x^(2)))dx` `=(x^(2))/(2)sin^(-1)x+(1)/(2)int(1-x^(2)-1)/(sqrt(1-x^(2)))dx` `rArr" "=(x^(2))/(2)sin^(-1)x+(1)/(2){int(1-x^(2))/(sqrt(1-x^(2)))dx-int(1)/(sqrt(1-x^(2)))dx}` `rArr ,=(x^(2))/(2)sin^(-1)x+(1)/(2){int sqrt(1-x^(2))dx-int(1)/(sqrt(1-x^(2)))dx}` `=(x^(2))/(2)sin^(-1)x+(1)/(2)[{(1)/(2)xsqrt(1-x^(2))+(1)/(2)sin^(-1)x}-sin^(-1)x]+C` `rArr l=(1)/(2)x^(2)sin^(-1)x+(1)/(4)xsqrt(1-x^(2))-(1)/(4)sin^(-1)x+C` |
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