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Let l_1=int_0^ooln(x+1/x)(dx)/(1+x^2) and l_2=int_0^(pi//2)(theta/(sintheta))^2 d theta, then which of the following is/are correct ? |
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Answer» `l_1 GT l_2` `[-theta^2 cot theta]_(0)^(pi//2)+int_0^(pi//2) 2 theta cot theta d theta` Use : INTEGRATION by parts `=-2 int_0^(pi//2) ln sin theta =piln2` `I_1=int_0^oo ln (x+1/x)(dx)/(1+x^2)` Let `tan^(-1) x = theta` `=int_0^(pi//2) ln (tan theta+cot theta)d theta` `=-int_0^(pi//2) (ln sin theta + ln cos theta ) d theta =pi ln2` `THEREFORE I_1=I_2` |
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