InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
`int_(pi//2)^(pi//2)(cosx)/(1+e^(x))dx` is equal toA. 1B. 0C. -1D. None of these |
|
Answer» Correct Answer - A `I-int _(-pi)^(pi//2)(cos x)/(1+e^(x))dx" (i)"` `I=int _(-pi)^(pi//2)(cos (pi//2-pi //2-x))/(1+e^((x//2-pi//2-x)))dx` `=int _(-pi)^(pi//2)(cos (-x))/(1+e^(-x))dx` `=int _(-pi)^(pi//2)^(e^(x)cos x)/(1+e^(x))dx` `=int _(-pi)^(pi//2)(e^(x)cos x)/(1+e^(x))dx" "(ii)` On adding Eqs. (i) and (ii), we get `2I=int_(-pi//2)^(pi//2)((1+e^(x))cos )/((1+e^(x)))dx` `int _(-pi//2)^(pi//2)cos x dx` `=2int _(0)^(pi//2)cos x dx` [Since, cos x is an even function.] `therefore 2I=2[sin x]_(0)^(pi//2)=2(1-0)=2` `impliesI=1` |
|