KCET2019MathematicsDefinite Integration
( ₀¹ 1+x 1-x d x= )
Options
- A( 2 +1 )
- B( 1 2 )
- C( 2 -1 )
- D( I 2 )
Correct answer
A. ( 2 +1 )
Step-by-step solution
(A) ( ₀¹ 1+x 1-x d x ) ( = ₀¹ (1+x)² (1+x)(1-x) d x ) ( = ₀¹ 1+x 1-x² d x ) ( = ₀¹ 1 1-x² + ₀¹ x d x 1-x² ) ( = [ ⁻¹ ]₀ ¹+ ₀¹ x d x 1-x² ) ( = ( 2 -0 )+ ₀¹ x d x 1-x² ) put ( 1-x²=t -2 x d x=d t ) ( x d x=- d t 2 ) at ( x=0 ; t=1 ) ( x=1 ; t=0 ) ( I= 2 + ₀¹ -d t 2 t ) ( = 2 +(- t )₁⁰= I 2 +(0+1)= I 2 +1 )