JEE Main 2026 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 2 April 2026, Shift 2, Maths Q17

Question 17 of 75 in this shift, Maths question 17 of 25, Section A.

The value of

\int_0^{20\pi} (\sin^4 x + \cos^4 x)dx

is equal to:

(1) $\frac{15\pi}{2}$
(2) $25\pi$
(3) $15\pi$ Official answer
(4) $\frac{25\pi}{2}$

Official answer

Option 3

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Periodic Function Property

Same idea in other shifts

Asked 6× in all

25 Jul 2022, Shift 1 · Q9For any real number $x$ , let $[x]$ denote the largest integer less than equal to $x$ . Let $f$ be a real valued function defined on the…HardSingle correct
26 Jul 2022, Shift 2 · Q9 $\int_0^{20\pi}\left(|\sin x|+|\cos x|\right)^2dx$ is equal toMediumSingle correct
30 Jul 2022, Shift 2 · Q71Let $A_k = \int_{k\pi}^{(k+1)\pi} e^{-x} \sin x\, dx$ , $k = 0, 1, 2, ..., 20$ . Then $\sum_{k=0}^{20} |A_k|$ is equal toHardSingle correct
28 Jun 2022, Shift 2 · Q8Let $f : \mathbf{R} \to \mathbf{R}$ be a continuous function satisfying $f(x)+f(x+k)=n$ , for all $x \in \mathbf{R}$ where $k>0$ and n is a…HardSingle correct
22 Jul 2021, Shift 2 · Q76If $\int_0^{100\pi}\frac{\sin^2x}{e^{\left(\frac{x}{\pi}-\left[\frac{x}{\pi}\right]\right)}}dx=\frac{\alpha\pi^3}{1+4\pi^2}$ ,…HardSingle 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.