JEE Main 2022 · MathsMultiple choiceSingle correctHardCalculation

JEE Main 28 July 2022, Shift 2, Maths Q70

Question 70 of 90 in this shift, Maths question 10 of 30, Section A.

The area enclosed by the curves

y=\log_e(x+e^2)

x=\log_e\left(\frac{2}{y}\right)

and

x=\log_e 2

, above the line

y=1

is :

(1) $2+e-\log_e 2$
(2) $1+e-\log_e 2$ Official answer
(3) $e-\log_e 2$
(4) $1+\log_e 2$

Official answer

Option 2

NTA final key.

Chapter: Application of Integrals
Topic: Area Under Curves
Idea tested: Exponential and Logarithmic Bounded Regions

Same topic in other shifts

All Area Under Curves questions

2 Apr 2026, Shift 2 · Q24If the area of the region bounded by $16x^2 - 9y^2 = 144$ and $8x - 3y = 24$ is $A$ , then $3(A + 6\log_e(3))$ is equal toHardNumerical value
4 Apr 2026, Shift 1 · Q18The area of the region $\{(x,y): y\le\pi-|x|,\ y\le|x\sin x|,\ y\ge0\}$ is:HardSingle correct
4 Apr 2026, Shift 2 · Q18The area of the region bounded by the curves $x+3y^2=0$ and $x+4y^2=1$ is equal to:EasySingle correct
5 Apr 2026, Shift 1 · Q16The area of the region $R = \{(x, y) : xy \leq 27,\ 1 \leq y \leq x^2\}$ is equal to:MediumSingle correct
5 Apr 2026, Shift 2 · Q24Let $f:\mathbf{R}\to\mathbf{R}$ be a function such that $f(x)+3f\left(\frac{\pi}{2}-x\right)=\sin x$ , $x \in \mathbf{R}$ . Let the maximum…HardNumerical value
6 Apr 2026, Shift 1 · Q19The area of the region $\{(x,y): 0\le y\le 6-x,\ y^2\ge 4x-3,\ x\ge 0\}$ is:MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.