Statement - I : The value of the integral ∫ π / 6 π / 3 d x 1 + tan   x is equal to…

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

Statement - II : ∫abfxdx=∫abfa+b-xdx.

  1. Statement - I is true; Statement - II is false.
  2. Statement - I is false; Statement - II is true.
  3. Statement - I true; Statement - II is true; Statement - II is a correct explanation for Statement - I.
  4. Statement - I is true; Statement - II is true; Statement - II is not a correct explanation for Statement - I.

Solution

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.

Asked in: JEE Main 2013 (07 Apr)

Practice more Definite Integration questions on Aicharya