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Let `A=int_(0)^(1)(e^(x))/(x+1)` dx then answer the following questions in terms of A. Q. `int_(0)^(1)((x)/(x+1))^(2)e^(x)dx` equalsA. `A-(e)/(2)`B. `(e)/(2)+1-A`C. `(e)/(2)+1-A`D. `(e)/(2)-A` |
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Answer» Correct Answer - C `int_(0)^(1)((x)/(x+1))^(2)e^(x)dx=int_(0)^(1)(((x+1)^(2)-(2x+1))/((x+1)^(2))).e^(x)dx` `I=int_(0)^(1)e^(x)dx-2int_(0)^(1)(e^(x))/(x+1)dx+int_(0)^(1)(1)/((x+1)^(2))e^(x)dx` `I=(e-1)-2A+(-(e)/(2)+1+A)=(e)/(2)-A` |
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