JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 10 April 2023, Shift 1, Maths Q8

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

I(x)=\int e^{\sin^2x}(\cos x\sin 2x-\sin x)\,dx

and

I(0)=1

, then

I\left(\frac{\pi}{3}\right)

is equal to

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

Official answer

Option 4

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Trigonometric Substitution

Same idea in other shifts

Asked 3× in all

6 Apr 2024, Shift 1 · Q11 $\int_0^{\pi/4}\frac{\cos^2 x\ \sin^2 x}{(\cos^3 x+\sin^3 x)^2}dx$ is equal toMediumSingle correct
3 Sep 2020, Shift 2 · Q61If the value of the integral $\int_0^{1/2} \frac{x^2}{(1 - x^2)^{3/2}} dx$ is $\frac{k}{6}$ , then k is equal to :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.