# 1-19 - January 19th 2005 Announcements Assigned reading for...

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January 19th, 2005 Announcements Assigned reading for the week: § 6.1, § 6.2 and § 6.3 First Midterm: Thursday, January 27, 2005 Sample midterms can be found at Today § 6.1: Areas between 2 curves. § 6.2: Volumes (slicing method). 1

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Problem: Consider the region S that lies between 2 curves y = f ( x ) and y = g ( x ) and between the vertical lines x = a and x = b , where f and g are continuous functions and f ( x ) g ( x ) for all x in [ a, b ]. Compute its area.
The area A of the region bounded by the curves y = f ( x ) and y = g ( x ) and between the vertical lines x = a and x = b , where f and g are continuous functions and f ( x ) g ( x ) for all x in [ a, b ] is A = b a [ f ( x ) - g ( x )] dx

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y -slicing” Sometimes it is better to divide the
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Unformatted text preview: area up into slices (thin rectangles) which are horizontal (i.e. parallel to the x-axis). The area A of the region bounded by the curves x = f ( y ) and x = g ( y ) and between the horizontal lines y = a and y = b , where f and g are continuous functions and f ( y ) ≥ g ( y ) for all y in [ a, b ] is A = Z b a [ f ( y )-g ( y )] dy The area A of the region bounded by the curves y = f ( x ) and y = g ( x ) and between the vertical lines x = a and x = b , where f and g are continuous functions in [ a, b ] is A = Z b a | f ( x )-g ( x ) | dx...
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