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The value of `int_(-pi//2)^(pi//2)(sin^(2)x)/(1+2^(x))dx` isA. `pi//4`B. `pi//8`C. `pi//2`D. `4pi` |
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Answer» Correct Answer - A `I=int_(-pi//2)^(pi//2) (sin^(2)x)/(1+2^(x))dx`…………….i or `I=int_(-pi//2)^(pi//2) (sin^(2)(-x))/(1+2^(-x))dx` or `I=int_(-pi//2)^(pi//2) (2^(x).sin^(2)x)/(2^(x)+1)dx`……………ii Adding i and ii we get `2I=int_(-pi//2)^(pi//2) sin^(2)xdx=2int_(0)^(pi//2) sin^(2)xdx` `=int_(0)^(pi//2)(1-cos^(2)x)dx` `=[x-(sin2x)/2]_(0)^(pi//2)=(pi)/2` `:. I=(pi)/4` |
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