JEE Main 2023 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 6 April 2023, Shift 2, Maths Q11

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

Let

f(x)

be a function satisfying

f(x)+f(\pi-x)=\pi^2,\ \forall x\in\mathbb{R}

. Then

\int_0^{\pi}f(x)\sin x\,dx

is equal to

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

Official answer

Option 4

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: King's Property

Same idea in other shifts

Asked 18× in all

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27 Jan 2024, Shift 1 · Q12If $(a, b)$ be the orthocentre of the triangle whose vertices are $(1, 2)$ , $(2, 3)$ and $(3, 1)$ , and $I_1=\int_a^b x\sin(4x-x^2)\,dx$ ,…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.