Section 6.1: Areas Between Curves If use ‘vertical’ rectangles whose base has a width of ∆ x : The area A of the region bounded by the curves y = f x ( 29 , y = g x ( 29 , and the lines x = a , x = b , where f and g are continuous and f x ( 29 ≥ g x ( 29 for a ≤ x ≤ b is A = f x ( 29 -g x ( 29 [ ] dx a b ∫ . The integrand should be expressed as upper curve minus lower curve. If use ‘horizontal’ rectangles whose base has a width of ∆ y : The area a of the region bounded by the curves x = f y ( 29 , x = g y ( 29 , and the lines y = c , y = d , where f and g are continuous and f y ( 29 ≥ g y ( 29 for c ≤ y ≤ d is A = f y ( 29-g y ( 29 [ ] dy c d ∫ . The integrand should be expressed as right-most curve minus left-most curve. Example. Determine the area bounded by the curves y = x 2 and y = x both ways. In other words, using ‘vertical’ rectangles and then using ‘horizontal’ rectangles.
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This note was uploaded on 01/12/2010 for the course MATH 44245 taught by Professor Famiglietti during the Fall '07 term at UC Irvine.