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The value of integral `I = int_(0)^(pi//4) (tan^(2)x + 2sin^(2)x) dx` is:A. 2B. 0C. `-(1)/(2)`D. `(1)/(2)` |
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Answer» Correct Answer - D The value ………. `I = overset(pi//4)underset(0)int (tan^(2)x+2sin^(2)x)dx` `= overset(pi//4)underset(0)int (sec^(2)x - 1+1-cos2x)dx` `= overset(pi//4)underset(0)int sec^(2)x dx - overset(pi//4)underset(0)int cos 2x dx` `=|tan x|_(0)^(pi//4) - |(sin2x)/(2)|_(0)^(pi//4)` `=(1-0) - ((1)/(2) - 0) = (1)/(2)` |
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