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Lecture

# 6.1 Areas Between Curves Question #1 (Easy)

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School
University of Toronto St. George
Department
Mathematics
Course
MAT136H1
Professor
all
Semester
Winter

Description
6.1 Integral Applications Area Between Two Functions Question #1 (Easy): Evaluating the Area Between Two Functions From the Graph Strategy The graph shows the shaded region bound by two functions ( ) and ( ) where ( ) ( )over the interval[ ]. The area of the shaded region is: ∫ [ ( ) ( ) ] . To evaluate, the interval has to be defined where the top and bottom function merges into a point. These are called the points of intersection and there must be at least two. This is determined by setting the functions equal to each other, and then solving for the unknown variable . Then which function lies at the top and bottom need to be determined in order to properly set the expression in the integral over . Sample Question Find the area of the shaded region bound by the functions and √ . Solution Two functions given are: and √ . From the graph the top and bottom functions are: √ and . So, ( ) √ and ( ) . Since the interval is not specified, point o
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