JEE Main 2024MathematicsArea Under CurvesMediumMCQ

JEE Main 2024 — Area Under Curves Question with Solution

JEE Main 2024 (31 Jan Shift 2)

Question

The area of the region enclosed by the parabola y=4x−x2 and 3y=x−42 is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C6

Step-by-step explanation

Given: y=4x-x2 and 3y=x-42

⇒4x-x2=x-423

⇒12x-3x2=x2+16-8x

⇒4x2-20x+16=0

⇒x2-5x+4=0

⇒x-4x-1=0

⇒x=4, 1

⇒y=0, 3

So, the intersection points are 4,0 and 1,3.

Area =∫144x−x2−x−423dx

Area =4x22−x33−x−43914

=642−643−42+13−279

=27−21=6

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 2024, 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.