AP EAMCET2015MathematicsDefinite Integration
_ -1 ^1 1+x+x^2 - 1-x+x^2 1+x+x^2 + 1-x+x^2 d x is equal to
Options
- A3 2
- B2
- C0
- D-1
Correct answer
C. 0
Step-by-step solution
I= _ -1 ^1 1+x+x^2 - 1-x+x^2 1+x+x^2 + 1-x+x^2 d x Let f(x)= 1+x+x^2 - 1-x+x^2 1+x+x^2 + 1-x+x^2 Replacing x by -x , we get aligned & f(-x)= 1-x+x^2 - 1+x+x^2 1-x+x^2 + 1+x+x^2 & = 1+x+x^2 - 1-x+x^2 1+x+x^2 + 1-x+x^2 =-f(x) aligned So, f(x) is an odd function. _ -1 ^1 f(x) d x=0