Question

If the value of the integral $\int\limits_1^2 e ^{ x ^2} dx$ is $\alpha$, then the value of $\int\limits_e^{e^4} \sqrt{\lambda n n x} dx$ is :

• A. $e^4-e-\alpha$
• B. $2 e ^4- e -\alpha$
• C. $2\left( e ^4- e \right)-\alpha$
• D. $2 e ^4-1-\alpha$

Answer 1

Answer: (B)

Put $\ln x=t^2 \Rightarrow x=e^{t^2} \Rightarrow d x=2 t^{t^2} d t$.
Hence $I=\int\limits_1^2 t .2 t^{t^2} d t$.
Now I.B.P. taking $t$ as the first function and $2 te ^{ t ^2}$ as the second function.