Area of a Region Between 2 Curves

# Area of a Region Between 2 Curves - you must find all...

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Area of a Region Between 2 Curves Section 7.1

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Area of a Region Between 2 Curves If f and g are continuous on [a, b] and g(x) < f(x) for all x in [a, b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is
[ ] dx x g x f A b a - = ) ( ) ( f g

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Representative rectangles are sometimes used. A vertical rectangle (of width ) implies integration with respect to x, whereas a horizontal rectangle (of width ) implies integration with respect to y. x y
If 2 curves intersect at more that 2 points, then to find the area of the region between the curves,

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Unformatted text preview: you must find all points of intersection and check to see which curve is above the other in each interval determined by these point. Look at Ex. 4 pg. 410 In general, to determine the area between 2 curves, you can use [ ] dx curve bottom curve top A x x ∫-= 2 1 ) ( ) ( [ ] dy curve left curve right A y y ∫-= 2 1 ) ( ) ( in variable x -vertical rectangles in variable y - horizontal rectangles Joke Time Why did the Easter egg hide? He was a little chicken! What do you get if you cross rabbits and termites? Bugs bunnies!...
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