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Lecture

6.1 Areas Between Curves Question #3 (Medium)

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Department
Mathematics
Course
MAT136H1
Professor
All Professors
Semester
Winter

Description
6.1 Integral Applications Area Between Two Functions Question #3 (Medium): Finding the Area Between Two Trigonometric Functions Strategy 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. Sample Question Fine the area of the region enclosed by the functions. Include the sketch of the bound region. , , Solution 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
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