int_1^2 frac{1}{x^2} e^{-frac{1}{x}} , dx = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $I = \int_1^2 \frac{1}{x^2} e^{-\frac{1}{x}} \, dx$. Substitute $t = -\frac{1}{x}$. Then,$dt = \frac{1}{x^2} \, dx$. When $x = 1$,$t = -1$. Wh

Vedclass · Accepted Answer

$\frac{e^{1/2} - 1}{e}$

Vedclass · Answer

(D) Let $I = \int_1^2 \frac{1}{x^2} e^{-\frac{1}{x}} \, dx$. Substitute $t = -\frac{1}{x}$. Then,$dt = \frac{1}{x^2} \, dx$. When $x = 1$,$t = -1$. When $x = 2$,$t = -\frac{1}{2}$. Substituting these into the integral: $I = \int_{-1}^{-1/2} e^t \, dt = [e^t]_{-1}^{-1/2}$. $I = e^{-1/2} - e^{-1} = \frac{1}{\sqrt{e}} - \frac{1}{e}$. $I = \frac{\sqrt{e} - 1}{e}$.

$\int_1^2 \frac{1}{x^2} e^{-\frac{1}{x}} \, dx = $

Similar Questions

Let $a, b, c$ be non-zero real numbers such that $\int_0^3 {(3ax^2 + 2bx + c)\,dx} = \int_1^3 {(3ax^2 + 2bx + c)\,dx}$,then

$\int_{0}^{\pi} \sin x \, dx = $ . . . . . . .

$\int_{0}^{2} |x - 1| \, dx = $

The value of $\int_{0}^{1} |3x^2 - 1| dx$ is

$\int_0^1 \sin^{-1} x \, dx = $ . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module