JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 30 July 2022, Shift 2, Maths Q71

Question 71 of 90 in this shift, Maths question 11 of 30, Section A.

Let

A_k = \int_{k\pi}^{(k+1)\pi} e^{-x} \sin x\, dx

k = 0, 1, 2, ..., 20

. Then

\sum_{k=0}^{20} |A_k|

is equal to

(1) $\left(\frac{e^{\pi}+1}{e^{\pi}-1}\right)\left(1 - e^{-20\pi}\right)$
(2) $\frac{1}{2}\left(\frac{e^{\pi}+1}{e^{\pi}-1}\right)\left(1 - e^{-21\pi}\right)$ Official answer
(3) $\left(\frac{e^{\pi}+1}{e^{\pi}-1}\right)\left(1 - e^{-21\pi}\right)$
(4) $\frac{1}{2}\left(\frac{e^{\pi}+1}{e^{\pi}-1}\right)\left(1 - e^{-20\pi}\right)$

Official answer

Option 2

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Periodic Function Property

Same idea in other shifts

Asked 6× in all

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.