JEE Main 2023MathematicsArea Under CurvesHardNumerical

JEE Main 2023 — Area Under Curves Question with Solution

JEE Main 2023 (11 Apr Shift 2)

Question

If A is the area in the first quadrant enclosed by the curve C:2x2-y+1=0, the tangent to C at the point 1, 3 and the line x+y=1, then the value of 60A is................

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Show full solutionCorrect answer: 16
Correct answer
16

Step-by-step explanation

Given,

y=2x2+1

Now tangent to above equation at 1,3 is given by,

y-3=4x-1

⇒y=4x-1

Now plotting the diagram we get,

Required area of bounded region will be,

A=∫012x2+1dx-area of △QOT -area of △PQR +area of △QRS

⇒A=23+1-12-98+940=1640

⇒60A=16

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About this question

This is a previous-year question from JEE Main 2023, 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.