JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 April 2025, Shift 2, Maths Q19

Question 19 of 75 in this shift, Maths question 19 of 25, Section A.

Let

(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 integral

I = \int_a^b \frac{9x^2}{1+5^x}\,\mathrm{d}x

is equal to :

(1) $18$
(2) $21$
(3) $24$ Official answer
(4) $27$

Official answer

Option 3

NTA final key.

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

Same idea in other shifts

Asked 10× 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
4 Apr 2024, Shift 2 · Q10If the value of the integral $\int_{-1}^{1}\frac{\cos\alpha x}{1+3^x}dx$ is $\frac{2}{\pi}$ . Then, a value of $\alpha$ isMediumSingle correct
1 Feb 2024, Shift 1 · Q27If $\int_{-\pi/2}^{\pi/2}\frac{8\sqrt{2}\cos x\,dx}{(1+e^{\sin x})(1+\sin^4 x)}=\alpha\pi+\beta\log_e(3+2\sqrt{2})$ , where $\alpha,\beta$ …HardNumerical value
29 Jan 2024, Shift 1 · Q11If the value of the integral…HardSingle correct
24 Jun 2022, Shift 2 · Q6The value of the integral $\int_{-\pi/2}^{\pi/2} \frac{dx}{(1+e^x)(\sin^6 x + \cos^6 x)}$ is equal toMediumSingle correct
25 Jun 2022, Shift 1 · Q2The value of $\int_0^{\pi} \frac{e^{\cos x}\sin x}{(1+\cos^2 x)(e^{\cos x}+e^{-\cos x})}\,dx$ is equal to :MediumSingle correct
27 Jun 2022, Shift 1 · Q10The value of the integral $\int_{-2}^{2} \frac{|x^3+x|}{(e^{x|x|}+1)}\,dx$ is equal to :MediumSingle correct
26 Aug 2021, Shift 2 · Q67The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{1+\sin^2 x}{1+\pi^{\sin x}}\right)\mathrm{d}x$ 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.