ReviewC6

ReviewC6 - Sections 6.1 6.2 and 6.3 Review Theory...

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Sections 6.1, 6.2 and 6.3: Review Theory Instructor: Ms. Hoa Nguyen ([email protected]) 6.1 The Area-between-Curves Problem : Find the area of the region S that lies between two curves y = f ( x ) and y = g ( x ) from a to b ( f ( x ) g ( x ) for all x in [ a, b ]). First, we approximate the region S by n rectangles (using left endpoints, right endpoints or mid- points x * i ). Then we take the limit of the sum of the areas of these rectangles (Riemann sum) as we increase the number of rectangles. So, define the actual area A of the region S to be the limit of the Riemann sum: A = lim n →∞ Σ n i =1 [ f ( x * i ) - g ( x * i )] 4 x = Z b a [ f ( x ) - g ( x )] dx 6.2 Disk/Washer Method The Volume Problem : Find the volume of a solid S that lies between x = a and x = b . First, we start slicing S ORTHOGONALLY to the axis of rotation (some horizontal line parallel to the x-axis in this case) to obtain n pieces. The base of each piece is a cross-section of S . The area of the cross-section can be approximated as the area of a disk
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ReviewC6 - Sections 6.1 6.2 and 6.3 Review Theory...

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