JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 9 January 2020, Shift 1, Maths Q63

Question 63 of 75 in this shift, Maths question 13 of 25, Section A.

The value of

\int_0^{2\pi}\frac{x\sin^8 x}{\sin^8 x+\cos^8 x}\,\mathrm{d}x

is equal to :

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

Official answer

Option 4

NTA final key (Jan 2020).

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

Same idea in other shifts

Asked 18× in all

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5 Apr 2024, Shift 1 · Q10The value of $\int_{-\pi}^{\pi}\frac{2y(1+\sin y)}{1+\cos^2 y}\,dy$ is :MediumSingle correct
5 Apr 2024, Shift 2 · Q25If $f(t) = \int_0^{\pi} \frac{2x\,dx}{1-\cos^2 t \sin^2 x}$ , $0 < t < \pi$ , then the value of…HardNumerical value
1 Feb 2024, Shift 1 · Q10The value of the intergral $\int_0^{\pi/4}\frac{x\,dx}{\sin^4(2x)+\cos^4(2x)}$ equals :HardSingle correct
1 Feb 2024, Shift 2 · Q11The value of $\int_{-0}^{1}(2x^3-3x^2-x+1)^{\frac{1}{3}}\,dx$ is equal to :MediumSingle correct
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.