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 ,
So the first integral looks like,
For the second interval ,
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 ...