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`((int (x)/(2))/(-(x)/(2)))log((2-sinx)/(2+sin x))` dx is equal toA. 1B. 3C. 2D. 0 |
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Answer» Correct Answer - D We have, `i=(underset(-x)overset((pi)/(2))int)/(2) log ((2-sin x)/(2+sin x))dx` `"Let " f(x)=log ((2-sinx)/(2+sin x))` Then, f(-x)=`log ((2-sin(-x))/(2+sin(-x)))` `=log ((2+sin x)/(2-sinx))=log ((2-sinx)/(2+sin x))^(-1)` `=-log ((2-sin x)/(2+sin x))=-f(x)` Then, f(x) is an odd function. `therefore (underset(pi)overset((pi)/(2))int (2) f(x)dx=0` `[therefore ` If f(x) is an odd function, then `underset(-a)overset(a) f(x)dx=0` |
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