JEE Main 2025 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 3 April 2025, Shift 1, Maths Q18

Question 18 of 75 in this shift, Maths question 18 of 25, Section A.

Let

f(x) = \int x^3\sqrt{3 - x^2}\,dx

. If

5f(\sqrt{2}) = -4

, then

f(1)

is equal to

(1) $-\frac{2\sqrt{2}}{5}$
(2) $-\frac{6\sqrt{2}}{5}$ Official answer
(3) $-\frac{4\sqrt{2}}{5}$
(4) $-\frac{8\sqrt{2}}{5}$

Official answer

Option 2

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Composite Function Substitution

Same idea in other shifts

Asked 5× in all

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16 Mar 2021, Shift 2 · Q81For real numbers $\alpha,\beta,\gamma$ and $\delta$ , if…HardNumerical value
18 Mar 2021, Shift 1 · Q73The integral $\int\dfrac{(2x-1)\cos\sqrt{(2x-1)^2+5}}{\sqrt{4x^2-4x+6}}\,dx$ is equal to : (where c is a constant of integration)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.