The value of the definite integral, ∫ limits0100 ( x / e x 2) dx is equal to

Question

The value of the definite integral, ∫ limits0100 ( x / e x 2) dx is equal to (A) (1/2)(1- e -10) (B) 2(1- e -10) (C) (1/2)( e -10-1) (D) (1/2)(1- e -104)

Tardigrade Admin · Accepted Answer

put x2=t ; x d x=(d t/2) .I =(1/2) ∫ limits0104 ( dt / e t )=-(1/2) e - t ]0104=(1/2)(1- e -104)

Q. The value of the definite integral, $0 \int 100 \frac{x}{e ^{x^{2}}} d x$ is equal to

$\frac{1}{2} (1 - e^{- 10})$

$2 (1 - e^{- 10})$

$\frac{1}{2} (e^{- 10} - 1)$

$\frac{1}{2} (1 - e^{- 1 0^{4}})$

put $x^{2} = t; x d x = \frac{d t}{2}$
$I = \frac{1}{2} 0 \int 1 0^{4} \frac{d t}{e ^{t}} = - \frac{1}{2} e^{- t}]_{0}^{1 0^{4}} = \frac{1}{2} (1 - e^{- 1 0^{4}})$

Q. The value of the definite integral, 0∫100​ex2x​dx is equal to

21​(1−e−10)

2(1−e−10)

21​(e−10−1)

21​(1−e−104)