AP Calculus BC Unit 6 Retake
Flashcard
•
Mathematics
•
11th - 12th Grade
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the formula for the volume of a solid of revolution when revolving around the y-axis?
Back
The volume V can be calculated using the formula: V = π∫[a to b] (f(x))^2 dx, where f(x) is the function being revolved.
2.
FLASHCARD QUESTION
Front
How do you find the volume of the solid generated by revolving the area bounded by y = x^2 and the x-axis from [0, 2] around the y-axis?
Back
Use the formula V = π∫[0 to 2] (x^2)^2 dx = π∫[0 to 2] x^4 dx = π[1/5 * x^5] from 0 to 2 = 8π.
3.
FLASHCARD QUESTION
Front
If velocity is negative and increasing, what can be said about the speed?
Back
The speed is decreasing because the object is moving in the negative direction but slowing down.
4.
FLASHCARD QUESTION
Front
What integral would allow you to find the volume of the region bounded by y = 2x^2 and y = 8 around the line y = 11?
Back
The integral is V = π∫[0 to 2] [(11 - 2x^2)^2 - 9] dx.
5.
FLASHCARD QUESTION
Front
What is the volume of the solid formed by revolving the region bounded by y = x and y = x^2 about the line y = 1?
Back
The volume is V = π/5.
6.
FLASHCARD QUESTION
Front
What is the relationship between velocity and speed when velocity is negative?
Back
Speed is the absolute value of velocity; thus, if velocity is negative, speed is positive but decreasing if the velocity is increasing.
7.
FLASHCARD QUESTION
Front
How do you set up the integral for finding the volume of a solid of revolution?
Back
Identify the function to be revolved, the axis of rotation, and the limits of integration, then use the appropriate volume formula.
Tags
CCSS.8.G.C.9
CCSS.HSG.GMD.A.3
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