If the value of the integral 0.05em( x^2 cos ⁡x1+ ^x+ 1+ sin^2 ⁡x1+e^ sin ⁡x^2033) dx= 4 ( +a )-2 , then the value of a is

Question

Accepted Answer

Correct answer: A. (a) I= 0.05em 0.05em( x^2 cos ⁡x1+ ^x+ 1+ sin^2 ⁡x1+e^ sin ⁡x^2023) dxI= 0.05em 0.05em( x^2 cos ⁡x1+ ^-x+ 1+ sin^2 ⁡x1+e^ sin ⁡ (-x )^2023) dx On Adding, we get 2I= 0.05em(x^2 cos ⁡x+1+ sin^2 ⁡x) dx On solving I= ^24+ 3 4-2a=3

$If the value of the integral \sum (\frac{x ^{2} cos x}{1 + π ^{x}} + \frac{1 + sin ^{2} x}{1 + e ^{sin x^{2033}}}) dx = \frac{π}{4} (π + a) - 2, then the value of a is$

Solution

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