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  4. The value of the definite integral, ∫0√ ln ((π/2)) cos ( e x 2)-2 xe x 2 dx is

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Q. The value of the definite integral, $\quad \int_0^{\sqrt{\ln \left(\frac{\pi}{2}\right)}} \cos \left( e ^{ x ^2}\right)-2 xe ^{ x ^2} dx$ is

Integrals

Solution:

put $e ^{ x ^2}= t ; \quad e ^{ x ^2} \cdot 2 xdx = dt \quad ; \quad \int\limits_1^{\pi / 2} \cos tdt =[\sin t ]_1^{\pi / 2}=1-(\sin 1)$