# How do you find the area of the region bounded by the curves #y=tan(x)# and #y=2sin(x)# on the interval #-pi/3<=x<=pi/3# ?

##### 1 Answer

We have a bit of work ahead of use with this problem. This is a definite integral problem.

First we need to identify the location(s) where these functions intersect. These will be the x-values and also define the upper and lower boundaries.

Factor out

Set each factor equal to zero to find the intersections.

The functions intersect at

Our 2 new intervals are

Now we need to figure out which function is greater over each of the 2 new intervals.

For the **first interval** ,

**Greater**

So the first integral looks like,

For the **second interval** ,

**Greater**

So the first integral looks like,

We now have to solve the following ...

Remember that

After entering this huge expression into the TI-84 C the results is as follows ...