Section5_1_review

Section5_1_review - Section 5.1 Areas The area problem is...

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Section 5.1: Areas The area problem is the problem of determining the area, A , of a region S that is bounded by a curve y = f x (29 and the x -axis as x goes from a to b . We can approximate the area of region S by dividing the interval a , b [ ] into n subintervals of equal width x = b - a n . This division of a , b [ ] also divides S into n subregions; the area of each subregion can be approximated by determining the area of the corresponding subrectangle. The subintervals are then x 0 , x 1 [ ] , x 1 , x 2 [ ] , K x n - 1 , x n [ ] , with x 0 = a and x n = b . If the right-side of each subinterval is used to determine the height of the corresponding subrectangle (i.e., the sample point is the right-side of each subinterval), then the area of region S is A f x i ( 29 x i = 1 n . (Note: This sum is called a Riemann sum.) If the left-side of each subinterval is used to determine the height of the corresponding subrectangle (i.e., the sample point is the left-side of each subinterval), then the area of region S is A f x i - 1 ( 29 x i = 1 n . (Note: This sum is called a Riemann sum.) If the midpoint of each subinterval is used to determine the height of the corresponding subrectangle (i.e., the sample point is the midpoint of each subinterval), then the area of region S is A f x i - 1 + x i 2 ∆ x i = 1 n . (Note: This sum is called a Riemann sum.) By letting x i * be the sample point, then A f x i * ( 29 x i = 1 n , where: x i * = x i if the sample point is the right-side, x i * = x i - 1 if the sample point is the left-side, and x i * = x i - 1 + x i 2 is the midpoint. Note:
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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.

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Section5_1_review - Section 5.1 Areas The area problem is...

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