InterviewSolution
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InterviewSolution
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If `f(x)=(sin^(-1)x)/(sqrt(1-x^(2))) and g(x)=e^(sin^(-1)x),` then `int f(x)g(x)dx` is equal toA. `e^(sin^(-1)x)(sin^(-1)x-1)+C`B. `e^(sin^(-1)x)+C`C. `e^((sin^(-1)x)^(2))+C`D. `e^(2sin^(-1)x)+C` |
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Answer» Correct Answer - A `intf(x)g(x)=int(sin^(-1)x)/(sqrt(1-x^(2)))e^(sin^(-1))dx` Put`" "sin^(-1)x=t` `rArr" "(1)/(sqrt(1-x^(2)))dx=dt` `therefore" "intf(x)g(x)dx=int te^(t)dt=te^(t)-e^(t)+C` `=e^(sin^(-1)x)(sin^(-1)x-1)+C` |
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