JEE Main 2013MathematicsDefinite IntegrationEasyMCQ

JEE Main 2013 — Definite Integration Question with Solution

JEE Main 2013 (07 Apr)

Question

Statement - I : The value of the integral ∫π/6π/3dx1+tan x is equal to π6.

Statement - II : ∫abfxdx=∫abfa+b-xdx.

Choose an option

Show full solutionCorrect option: B
Correct answer
BStatement - I is false; Statement - II is true.

Step-by-step explanation

Statement II is a standard property of definite integrals.

For statement I : I=∫π/6π/3dx1+tan x=∫π/6π/3dx1+cot x

I=∫π/6π/3tan x1+tan xdx=∫π/6π/3sinxcosx+sinxdx=∫π/6π/3cosxcosx+sinxdx

2I=∫π/6π/3dx

2I=π3-π6

I=π12

Hence, statement I is false.

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About this question

This is a previous-year question from JEE Main 2013, 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.