Question

How do you find the area under the graph of `f(x)=sin(x)` on the interval `[-pi,pi]` ?

Answer 1

For this question to have to set up a definite integral.

We see that this integral is bounded from `-pi` to `pi` inclusive.

Also remember that after we integrate we have to subtract the result of the lower bound, `-pi` from that of the higher bound, `pi`.

Be careful with all of those double negatives which resolve to positives.

Lastly, remember from the unit circle that both `cos(-pi)` and `cos(pi)` resolve to -1.

`int_(-pi)^pi sin(x) dx`

`=[-cos(x)]_-pi^pi=-cos(pi)-(-cos(-pi))`

`=-(-1)-(-(-1))=1-1=0`

Watch this problem solved here.