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JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 June 2022, Shift 2, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

Let

f

be a differentiable function in

\left(0,\frac{\pi}{2}\right)

. If

\int_{\cos x}^{1}t^2f(t)\,dt=\sin^3x+\cos x

, then

\frac{1}{\sqrt{3}}f'\left(\frac{1}{\sqrt{3}}\right)

is equal to

(1) $6-9\sqrt{2}$
(2) $6-\frac{9}{\sqrt{2}}$ Official answer
(3) $\frac{9}{2}-6\sqrt{2}$
(4) $\frac{9}{\sqrt{2}}-6$

Official answer

Option 2

NTA final key.

Chapter: Integrals
Topic: Leibniz Rule
Idea tested: Variable Limit Leibniz

Same idea in other shifts

Asked 2× in all

30 Jun 2022, Shift 1 · Q25Let $f(t) = \int_0^t e^{x^3}\left(\frac{x^8}{(x^6 + 2x^3 + 2)^2}\right) dx$ . If $f(1) + f'(1) = \alpha e - \frac{1}{6}$ , then the value of…HardNumerical value

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.