JEE Main 2014MathematicsArea Under CurvesEasyMCQ

JEE Main 2014 — Area Under Curves Question with Solution

JEE Main 2014 (09 Apr Online)

Question

Let A=x,y:y2≤4x, y-2x≥-4. The area of the region A in square units is

Choose an option

Show full solutionCorrect option: C
Correct answer
C9

Step-by-step explanation

Given, y2=4x   ...1

y=2x−4⇒2x=y+4   ...2

Solving equations 1 & 2, we get

⇒y2=2y+8

⇒ y2-2y-8=0

⇒y-4y+2=0

⇒y=4, -2

From equation 2,

If y=4 then x=4 and if y=-2 then x=1.

A=∫044x dx-12×2×4+∫014xdx+12×1×2

=2x3/23204-4+2x3/23201+1

=438-4+431+1

=363-3

=9

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About this question

This is a previous-year question from JEE Main 2014, 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.