AP Multiple Choice Area & Volume Problems

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•
Mathematics
•
12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the formula for the area between two curves y=f(x) and y=g(x) from x=a to x=b?
Back
The area A is given by A = \int_{a}^{b} (f(x) - g(x)) \, dx, where f(x) is the upper curve and g(x) is the lower curve.
2.
FLASHCARD QUESTION
Front
How do you find the volume of a solid of revolution using the disk method?
Back
The volume V is given by V = \pi \int_{a}^{b} [f(x)]^2 \, dx, where f(x) is the function being revolved around the x-axis.
3.
FLASHCARD QUESTION
Front
What is the washer method for finding volumes of solids of revolution?
Back
The volume V is given by V = \pi \int_{a}^{b} ([R(x)]^2 - [r(x)]^2) \, dx, where R(x) is the outer radius and r(x) is the inner radius.
4.
FLASHCARD QUESTION
Front
What is the formula for the volume of a solid generated by revolving a region around the y-axis?
Back
The volume V is given by V = \pi \int_{c}^{d} [f(y)]^2 \, dy, where f(y) is the function expressed in terms of y.
5.
FLASHCARD QUESTION
Front
How do you determine the limits of integration when finding the area between curves?
Back
The limits of integration are found by solving the equation f(x) = g(x) to find the points of intersection.
6.
FLASHCARD QUESTION
Front
What is the significance of the first quadrant in area and volume problems?
Back
The first quadrant is where both x and y are non-negative, simplifying calculations for area and volume.
7.
FLASHCARD QUESTION
Front
What is the relationship between the area under a curve and the volume of a solid of revolution?
Back
The area under a curve can be used to calculate the volume of a solid of revolution by integrating the area of circular disks or washers.
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