KCET2013MathematicsDefinite Integration
If I₁= ₀^ / 2 x x d x and I₂= ₀^ / 2 x x d x , then which one of the following is true?
Options
- AI₁=I₂
- BI₁+I₂=0
- CI₁= 2 I₂
- DI₁+I₂= 2
Correct answer
D. I₁+I₂= 2
Step-by-step solution
Given, aligned I₁ &= ₀^ / 2 x x d x and I₂= ₀^ / 2 x x d x Now, l₁ &=[x(- x)]₀^ / 2 - ₀^ / 2 1 (- x) d x &=[0+0]+[ x]₀^ / 2 =1 and l₂ &=[x x]₀^ / 2 - ₀^ / 2 1 x d x &= [ 2 -0 ]-[- x]₀^ / 2 &= 2 +(0-1)= 2 -1 & l₁+I₂= 2 aligned