JEE Main 2019MathematicsArea Under CurvesHardMCQ

JEE Main 2019 — Area Under Curves Question with Solution

JEE Main 2019 (09 Jan Shift 1)

Question

The area (in sq. units) bounded by the parabola y=x2-1, the tangent at the point 2,3 to it and the y-axis is

Choose an option

Show full solutionCorrect option: B
Correct answer
B83

Step-by-step explanation

We have, dydx=2x

∴ Slope of tangent at 2,3 is

m=4

∴ Equation of tangent is y-3=4x-2

∴ Point T≡0,-5

∴ Area of ΔPTM=12×8×2=8

Area of curve PAMP=∫-13y+1dy

=23y+132-13=163

∴ Required shaded area =8-163=83

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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.