Question

How do you find the area under the graph of `f(x)=cos(x)` on the interval `[-pi/2,pi/2]` ?

Answer 1

This is an integration problem. We will find the area under the curve `cos(x)` over the interval `[-pi/2,pi/2]`. This is inclusive because of the square brackets.

On the unit circle remember that the positive side of y-axis corresponds to `pi/2` and a coordinate of `(0,1).` The y-coordinate corresponds to `1.`

On the unit circle remember that the negative side of y-axis corresponds to `-pi/2` and a coordinate of `(0,-1).` The y-coordinate corresponds to `-1.`

`int_(-pi/2)^(pi/2)cos(x) dx`

`=[sin(x)]_(-pi/2)^(pi/2)=[sin(pi/2)-sin(-pi/2)]=1-(-1)=2`

Watch this problem solved here