JEE Main 30 June 2022, Shift 1, Maths Q25

Question 25 of 90 in this shift, Maths question 25 of 30, Section B.

Let

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

150\alpha

is equal to __________.

Official answer

NTA final key.

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

Same idea in other shifts

Asked 2× in all

27 Jun 2022, Shift 2 · Q8Let $f$ 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…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 108 of the 174 JEE Main shifts held from 2017 to 2026.