InterviewSolution
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InterviewSolution
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`inte^(sin theta)[log sin theta+"cosec"^(2)theta]cos theta d theta` is equal toA. `inte^(sin theta)[log sin theta+"cosec"^(2)theta]+C`B. `e^(sin theta)[log sin theta+"cosec "theta]+C`C. `e^(sin theta)[log sin theta-"cosec "theta]+C`D. `e^(sin theta)[log sin theta - "cosec"^(2) theta]+C` |
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Answer» Correct Answer - C Let `l=inte^(sin theta)(log sin theta)cos theta d theta+int e^(sin theta)"cosec"^(2)thetacos theta d theta` Put `sin theta = t rArr cos theta d theta = dt` `therefore" "l=int e^(t) log t dt +int e^(t)t^(-2)dt` `=logt e^(t)-int(e^(t))/(t)dt+(e^(t)t^(-1))/(-1)-int(e^(t)t^(-))/(-1)dt` `=e^(t)(logt-(1)/(t))+c` `=e^(sin theta)(log sin theta - "cosec" theta )+C` |
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