JEE Main 2019MathematicsArea Under CurvesMediumMCQ

JEE Main 2019 — Area Under Curves Question with Solution

JEE Main 2019 (12 Apr Shift 1)

Question

If the area (in sq. units) of the region x, y: y2≤4x, x+y≤1, x≥0, y≥0 is a2+b, then a-b is equal to

Choose an option

Show full solutionCorrect option: A
Correct answer
A6

Step-by-step explanation


The given equations are,

y2=4x & x+y=1

⇒y2=41-y

⇒y2+4y-4=0 ⇒y=22-2

∴ Required Area =∫022-21-y-y24dx=y-y22-y312022-2

=22-2-22-222-22-2312-0

=22-21-2-1-2-123=-103+823

⇒-103+823=a2+b ⇒a=83, b=-103
∴ a-b=83+103=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 2019, 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.