152midterm2summary.pdf - Winter 2019 Math 15200 Section 42 Midterm 2 Review Sheet Section 6.1 Areas obtained by integration with respect to x and y Goal

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

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Winter 2019 Math 15200 Section 42 Midterm 2 Review Sheet Section 6.1 Areas obtained by integration with respect to x and y Goal : Understand how to find the area of a region bounded by graphs of equations by integrating with respect to x and y . Q. 1, 3, 7, 13, 17, 19, 21, 25, 31 Areas obtained by integration with respect to x Let Ω be the region between x = a and x = b bounded above by the graph y = f ( x ) and bounded below by the graph y = g ( x ). Then the area of Ω is Z b a [ f ( x ) - g ( x )] dx. Areas obtained by integration with respect to y Let Ω be the region between y = c and y = d bounded on the left by the graph x = G ( y ) and bounded on the right by the graph x = F ( y ). Then the area of Ω is Z d c [ F ( y ) - G ( y )] dy. Section 6.2 Solid of revolution: Disk / Washer method Goal : Understand how to find the volume of the solid of revolution using the disk/washer method. Let Ω be the region between x = a and x = b bounded above by the graph y = f ( x ) and bounded below by the graph y = g ( x ). If we revolve Ω about the x -axis, the solid obtained has volume Q. 1, 3, 7, 9, 11, 13, 15 V = Z b a π ([ f ( x )] 2 - [ g ( x )] 2 ) d x .

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