JEE Main 2022 · 28 Jul · Shift 2 · Mathematics Q70

MathematicsSingle correct+4 / -1Question 70 of 90

The area enclosed by the curves $y=\log_e\left(x+e^2\right)$ , $x=\log_e\left(\dfrac2y\right)$ and $x=\log_e2$ , above the line $y=1$ is :

2+e-\log_e2

1+e-\log_e2

e-\log_e2

1+\log_e2

Answer and worked solution

Official answer: B

Region (y from 1 to 2) between $x=e^y-e^2$ and $x=\ln\frac2y$ ; they meet at (0, 2), and at y = 1 the right curve reaches $x=\ln2$ .

Area $\int_1^2\left(\ln2-\ln y-e^y+e^2\right)dy=1+e-\ln2$ .

(B)

Topics:Area between curves

JEE Main 2022 · 28 Jul · Shift 2, Mathematics question 70