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Evaluate: `int_(pi//6)^(pi//4)(1+cotx)/(e^(x)sinx) dx` |
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Answer» Correct Answer - `2e^(-pi//6)-sqrt(2)e^(-pi//4)` `I=int_(pi//6)^(pi//4) e^(-x)(cosecx+cot x cosec x)dx` Put `x=timpliesdx=-dt` `:. I=-int_(-pi//6)^(-pi//4) e^(t)(-cosect+cot.cosec)dt` `=int_(-pi//6)^(-pi//4)e^(t)(cosect-cot t. cosec t)dt` `=e^(t)cosec t|_(-pi//6)^(-pi//4)` `=-sqrt(2)e^(-pi//4)+2d^(-pi//6)` `=2e^(-pi//6)-sqrt(2)e^(-pi//4)` |
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