Area Between Two Curves
Disk/Washer Method
Shell Method
100
Explain how you find the limits of integration when calculating the area between two curves
What is set the two functions equal to each other and use Algebra to solve
100
How can you tell to use the disk method in determining the volume of a region?
What is if there is only one function that makes up the region.
100
Using the shell method, if we rotate the region about the y-axis, would we integrate with respect to x or y?
What is "dx"
200
When there are multiple points of intersection between two functions, what must be done to calculate the area between the two functions?
What is split the area into two (or more) integrals and add together to get total volume.
200
Give the formula for the cross-sectional area for the washer method
What is (outer radius)^2 - (inner radius)^2
200
How can you tell which function goes first if there are multiple functions while using the shell method
What is the "greatest" or "furthest" function goes first.
300
DAILY DOUBLE: Congratulations! You just earned your team 300 pts.
300
DAILY DOUBLE FAILURE: We are sorry but you have lost 300 pts for your team. If you complain, you lose another 300 pts.
300
If we have the integral from 0 to pi/2 of 2pix^5 dx, describe the solid that is being rotated and over what axis the rotation is
What is f(x) = x^4 and the y-axis.
400
Explain, in general, how you tell which function goes first in your integral calculation when calculating the area between two curves
What is in general, the "upper" function goes first and the "lower" function goes second.
400
Using the washer method, if we were rotating the region around the line y = 2, would I differentiate with respect to x or y?
What is "dx"
400
If we are rotating the region about the line x = 2, what would the radius be of the function while using the shell method?
What is (2 - x)
500
Using sample point notation, write an expression using sigma notation and a limit that describes the area between two curves.
What is see smart board
500
Using the washer method, if we rotate the region over the line x = -2, give a possible integration set up of what the integral might look like.
What is answers will vary. See smart board.
500
Describe why the shell method is usually a more efficient method compared to the washer method.
What is the shell method is quicker and it doesn't involve an outer radius minus an inner radius.
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