MAT136H1 Lecture : 6.1 Areas Between Curves Question #3 (Medium)
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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. The graph of the functions is as follows: Setting the functions equal to each other to find the point of intersection: From algebraic standpoint, it makes sense to integrate over . +, lies at the top, and over * lies at the top, meaning the functions switch places over the whole interval, the integral needs to be split accordingly:
