Unit_V_Big_Ideas - Calculus 12 AP Unit V Review of Big...

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Calculus 12 AP Review of Big Ideas Unit V page 1 Calculus 12 AP Unit V Review of Big Ideas Concept I Area Region A Region B Region C Region D Area = f x ( ) dx a b Area = f y ( ) dy c d Area = f x ( )- g x ( ) ( ) dx a b Area = f y ( ) - g y ( ) ( ) dy c d General Comments • Notice that a and b are on the x -axis c and d are on the y -axis • When using formulas involving f x ( ) you must solve for y for example: y = x 2 • When using formulas involving f y ( ) you must solve for x for example: y = x 2 x = y • Look at the region and decide which way to slice vertical slices dx to x - axis horizontal slices dy to y - axis • Remember if using horizontal slices, write relations in the form " x =" • If finding total volume, sometimes it is necessary to break up your integrals, for example Area = f x ( ) dx - a b f x ( ) dx b c (See Assignments V-1 and V-2 for good questions on area to practice)
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Calculus 12 AP Review of Big Ideas Unit V page 2 Concept II Volume A Volumes of Revolution General Comments • These are based on circular slices therefore all of the formulas involve π r 2 • Try to visualize the slice, then rotate it around the line specified - then decide if it is a disk r 2 - or if it is a washer R 2 - r 2 • When revolving around the x -axis take vertical slices • When revolving around the y -axis take horizontal slices Region A Region B Region C Region D When revolving Region A around x -axis visualize the disk Volume = f x ( ) ( ) 2 dx a b When revolving Region B around y- axis visualize the disk Volume = f y ( ) ( ) 2 dy c d When revolving Region C around x- axis visualize the washer V = f x ( ) 2 - g x ( ) 2 ( ) dx a b When revolving Region D around y- axis visualize the washer V = f y ( ) 2 - g y ( ) 2 ( ) dy c d
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Calculus 12 AP Review of Big Ideas Unit V page 3 Revolving Regions Around lines Parallel to the Axes • When revolving around lines parallel to the x -axis and y -axis draw a diagram to determine the value of R and r in the formula for the washer. It is often helpful to think of a point on the curve in the form x , y ( ) and to use the distances x and y in your formulas for R and r , then translate them using the function. For example, in the above diagram if the region being rotated is under the curve between
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This note was uploaded on 02/04/2011 for the course MATH 116 taught by Professor John during the Spring '10 term at Saint Michael's College - Colchester, Vermont.

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Unit_V_Big_Ideas - Calculus 12 AP Unit V Review of Big...

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