Section6_1_review - Section 6.1 Areas Between Curves x If...

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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.
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