InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Examples: `int_(-pi/2) ^(pi/2) sin^2x dx` |
|
Answer» Let `f(x)=sin^(2)x`. Then, `f(-x)=[sin(-x)^(2)]=(-sinx)^(2)=sin^(2)x=f(x)`. `:.f(x)` is an even function. So, `int_(-pi//2)^(pi//2)sin^(2)xdx=2int_(0)^(pi//2)sin^(2)xdx=2int_(0)^(pi//2)((1-cos2x)/(2))dx` `=int_(0)^(pi//2)(1-cos2x)dx=[x-(sin2x)/(2)]_(0)^(pi//2)=(pi)/(2)`. |
|