If the value of the integral ∫ limits12 e x 2 dx is α, then the value of ∫ limitsee4 √λ n n x dx is :

Question

If the value of the integral ∫ limits12 e x 2 dx is α, then the value of ∫ limitsee4 √λ n n x dx is : (A) e4-e-α (B) 2 e 4- e -α (C) 2( e 4- e )-α (D) 2 e 4-1-α

Tardigrade Admin · Accepted Answer

Put ln x=t2 ⇒ x=et2 ⇒ d x=2 tt2 d t. Hence I=∫ limits12 t .2 tt2 d t. Now I.B.P. taking t as the first function and 2 te t 2 as the second function.

Q. If the value of the integral $1 \int 2 e^{x^{2}} d x$ is $α$ , then the value of $e \int e^{4} λnn x d x$ is :

$e^{4} - e - α$

$2 e^{4} - e - α$

$2 (e^{4} - e) - α$

$2 e^{4} - 1 - α$

Put $ln x = t^{2} \Rightarrow x = e^{t^{2}} \Rightarrow d x = 2 t^{t^{2}} d t$ .
Hence $I = 1 \int 2 t .2 t^{t^{2}} d t$ .
Now I.B.P. taking $t$ as the first function and $2 t e^{t^{2}}$ as the second function.

Q. If the value of the integral 1∫2​ex2dx is α, then the value of e∫e4​λnnx​dx is :

e4−e−α

2e4−e−α

2(e4−e)−α

2e4−1−α