6_1 - Section 6.1: Areas between curves Instructor: Ms. Hoa...

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Section 6.1: Areas between curves Instructor: Ms. Hoa Nguyen (nguyen@scs.fsu.edu) The Area Problem Special Case : Find the area of the region S that lies between two curves y = f ( x ) and y = g ( x ) from a to b ( f , g are continuous functions and f ( x ) g ( x ) for all x in [ a, b ]). This means that S is bounded by the graphs of continuous functions f , g , the vertical lines x = a and x = b . The method Divide S into n strips of equal width 4 x = b - a n . Then we have n subintervals: [ x 0 , x 1 ] , [ x 1 , x 2 ] , [ x 2 , x 3 ] , · · · , [ x n - 1 , x n ] where x 0 = a and x n = b . Approximate the i th strip by a rectangle with base 4 x and height f ( x * i ) - g ( x * i ). The sample points x * i can a right endpoint, left endpoint or any point in the i th subinterval [ x i - 1 , x i ]. The Riemann sums are R n = ( f - g )( x 1 ) 4 x + ( f - g )( x 2 ) 4 x + · · · + ( f - g )( x n ) 4 x = Σ n i =1 ( f - g )( x i ) 4 x if the right endpoints are used. L
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6_1 - Section 6.1: Areas between curves Instructor: Ms. Hoa...

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