# 152midterm2summary.pdf - Winter 2019 Math 15200 Section 42...

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Winter 2019 Math 15200 Section 42Midterm 2 Review SheetSection 6.1Areas obtained by integration with respect toxandyGoal: Understand how to find the area of a region bounded by graphs of equations by integrating with respecttoxandy.Q. 1, 3, 7, 13, 17, 19, 21, 25, 31Areas obtained by integration with respect toxLet Ω be the region betweenx=aandx=bbounded above by the graphy=f(x) and bounded below by thegraphy=g(x). Then the area of Ω isZba[f(x)-g(x)]dx.Areas obtained by integration with respect toyLet Ω be the region betweeny=candy=dbounded on the left by the graphx=G(y) and bounded on theright by the graphx=F(y). Then the area of Ω isZdc[F(y)-G(y)]dy.Section 6.2Solid of revolution: Disk / Washer methodGoal: Understand how to find the volume of the solid of revolution using the disk/washer method.Let Ω be the region betweenx=aandx=bbounded above by the graphy=f(x) and bounded below by thegraphy=g(x). If we revolve Ω about thex-axis, the solid obtained has volumeQ. 1, 3, 7, 9, 11, 13, 15V=Zbaπ([f(x)]2-[g(x)]2)dx.

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