&integral;@Sub{0}@Sup{@DIV{π;2}} tan X^2 dxthe answer is 1- pi/4 how is it done

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cosinusix eNotes educator| Certified Educator

If the question is to find the `I=int_0^(pi/4) tan x^2 d x`

Use the formula `tan'x=1+tan^2 x`

Then `tan^2x=tan'x-1`

And antiderivative of `tan^2x` is `tan x-x`

Integrate it between 0 and pi/4

` `

`I=tan(pi/4)-tan 0-pi/4+0=1-pi/4`` `

 

Solution `I=1-pi/4` ` `