Question

The value of the definite integral, ${\int }_0^{\sqrt{\ln \left(\frac{\pi }{2}\right)}}\cos \left(e^{x^2}\right)-2x{e}^{x^2}dx$ is

• A. 1
• B. $1+(\sin 1)$
• C. $1-(\sin 1)$
• D. $(\sin 1)-1$

Answer 1

Answer: (C)

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