JEE Main 2018MathematicsArea Under CurvesHardMCQ

JEE Main 2018 — Area Under Curves Question with Solution

JEE Main 2018 (08 Apr)

Question

Let gx=cosx2, fx=x, and α,βα<β be the roots of the quadratic equation 18x2-9πx+π2=0. Then the area (in sq. units) bounded by the curve y=gofx and the lines x=α,x=β and y=0, is

Choose an option

Show full solutionCorrect option: B
Correct answer
B123-1

Step-by-step explanation

Given, gx=cosx2, fx=x

Given quadratic is 18x2-9πx+π2=0

The roots are x=9π±81π2-72π22×18

⇒x=9π±9π236

⇒x=9±3π36

⇒x=π3, π6

y=gofx=cosx2=cosx

Required Area =∫π6π3cos⁡x dx=sinxπ6π3
⇒ 32-12

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Area Under Curves chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2018, covering the Area Under Curves chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.