2Bsection5_6part1 - A r e a b e tw e e n 2 c u r v e s S e...

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Area between 2 curves. Section 5.6 Part 1
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upper function lower function PROBLEM 1 Given 2 functions of x: y=f(x) and y=g(x), defined over [a,b], find the area of the region enclosed between the 2 graphs. ANSWER right‐most value of x left‐most value of x A=?
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Areas between 2 functions as Riemann Sum: The height of a rectangle is of the form f(x)‐g(x), where f is the upper curve, and g is the lower one.
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Right function Left function PROBLEM 2 Given 2 functions of y: x=f(y) and x=g(y), defined over [c,d], find the area of the region enclosed between the 2 graphs. ANSWER biggest value of y smallest value of y A=?
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Right function: x=f(y) left function: x=g(y) We use horizontal rectangles. The height of a rectange is f(y)‐g(y), where f is the right curve and f is the left one.
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? ? You need the graphs!
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upper function lower function Look at the graph ? ? ? What about a and b? They are the x‐coordinates of the points where the 2 curves intersect.
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