6.1 Integral Applications
Area Between Two Functions
Question #3 (Medium): Finding the Area Between Two Trigonometric Functions
When trigonometric functions are given, determining the points of intersection to set the interval for
integral is no different. Still set two functions equal to each other to find the values. Usually the interval
given in the question matches the algebraically determined points of intersection. Observe symmetrical
behavior if there exists one and simplify the integral as much as possible. Determine which function lies
at the top and bottom. Sometimes the interval needs to be split because the functions switch places.
Fine the area of the region enclosed by the functions. Include the sketch of the bound region.
The graph of the functions is as follows:
Setting the functions equal to each other to find the point of intersection:
. Rewriting the left side: . Moving