JEE Main 2016MathematicsDefinite IntegrationMediumMCQ

JEE Main 2016 — Definite Integration Question with Solution

JEE Main 2016 (10 Apr Online)

Question

The value of the integral ∫410x2x2−28x+196+x2dx, where x denotes the greatest integer less than or equal to x, is

Choose an option

Show full solutionCorrect option: D
Correct answer
D3

Step-by-step explanation

Let I= ∫410x2x2-28x+196+x2dx

⇒I= ∫410x214-x2+x2 dx   ...i

Use ∫abfxdx=∫abfa+b-xdx

I= ∫41014-x2x2+14-x2 dx   ...ii 

By adding equations i & ii, we get

2I= ∫41014-x2+x2x2+14-x2 dx

⇒2I= ∫410dx

⇒2I=6 

⇒I=3

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Definite Integration 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 2016, covering the Definite 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.