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`int_(-pi/2)^(pi/2)(e^(|sinx|)cosx)/((1+e^(tanx))dxi se q u a lto``e+1`(b) `1-e``e-1`(d) none of theseA. `e+1`B. `2e`C. `e-1`D. `e-2` |
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Answer» Correct Answer - C `I=int_(-pi//2)^(pi//2) (e^(|sinx|)/cosx)/(1+e^(tanx))dx` ……….1 `=int_(-pi//2)^(pi//2) (e^(|sin(-x)|)cos(-x))/(1+e^(tan(-x)))dx` `:. I=int_(-pi//2)^(pi//2) (e^(tanx)e^(|sinx|)cosx)/(e^(tanx)+1)dx`………………2 Adding 1 and 2 we get `2I=int_(-pi//2)^(pi/2) e^(|sinx|)cosx dx` `=2int_(0)^(pi//2)e^(sinx)cosx dx` `=2[e^(sinx)]_(0)^(pi//2) =2(e-1)` `:. I=e-1` |
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