JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 29 January 2024, Shift 1, Maths Q11

Question 11 of 90 in this shift, Maths question 11 of 30, Section A.

If the value of the integral

\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{x^2\cos x}{1+\pi^x}+\frac{1+\sin^2x}{1+e^{\sin x^{2023}}}\right)dx=\frac{\pi}{4}(\pi+a)-2

, then the value of

a

(1) $2$
(2) $-\frac{3}{2}$
(3) $\frac{3}{2}$
(4) $3$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Symmetric Limits with Exponential Denominator Trick

Same idea in other shifts

Asked 3× in all

6 Apr 2026, Shift 1 · Q18The value of the integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\left(\frac{32\cos^4 x}{1+e^{\sin x}}\right)dx$ is:MediumSingle correct
2 Apr 2025, Shift 2 · Q19Let $(a, b)$ be the point of intersection of the curve $x^2 = 2y$ and the straight line $y - 2x - 6 = 0$ in the second quadrant. Then the…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 42 of the 174 JEE Main shifts held from 2017 to 2026.