Question

The value of ${\int }_0^{\frac{\pi }{2}}{e}^{\sin x}\cdot \cos x\mathrm{dx}$ is equal to

• A. e - 1
• B. e + 1
• C. e - 2
• D. e + 2

Answer 1

The correct option is A e - 1

${\int }_0^{\frac{\pi }{2}}{e}^{\sin x}\cdot \cos x\mathrm{dx}\mathrm{Let}\sin x=t\Rightarrow \cos x\mathrm{dx}=\mathrm{dt}\mathrm{If}x=0,t=0\mathrm{and}\mathrm{if}x=\frac{\pi }{2},t=1{\int }_0^1{e}^t\mathrm{dt}={\left(e^t\right]}_0^1=e^1-e^0=e-1$