JEE Main 2019MathematicsIndefinite IntegrationMediumMCQ

JEE Main 2019 — Indefinite Integration Question with Solution

JEE Main 2019 (10 Apr Shift 1)

Question

If ∫dxx2-2x+102=Atan-1x-13+fxx2-2x+10+C, then (where C is a constant of integration)

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Show full solutionCorrect option: D
Correct answer
DA=154 and fx=3x-1

Step-by-step explanation

We have I=∫dxx2-2x+102=∫dxx-12+322

Let x –1=3tanθ⇒dx=3sec2θdθ

⇒I=∫3sec2θdθ81sec4θ=127∫cos2θdθ

=154∫1+cos2θdθ

=154θ+sin2θ2+C

=154θ+sinθcosθ+C, where C is the constant of integration.

=154tan-1x-13+x-131+x-132+C

=154tan-1x-13+3x-1x2-2x+10+C

Hence, A=154 & fx=3(x-1)

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About this question

This is a previous-year question from JEE Main 2019, covering the Indefinite Integration 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.