For problem 6, isn't the radius of the disc (9 - y), not (9 - y^2)? The explanation says you can "see this from the graph" but what I see is [9 - f(x)] and f(x) = Y; therefore, r = (9 - y), right?

f(x)=√x, not y. You should be integrating π∫[9-f(y)]dy. The given curve is y=√x, but if we're going to evaluate an integral using dy then our equation also has to be in terms of y. If we square both sides of y=√x, we get y²=x. So f(y)=y², and our radius r=9-f(y) is 9-y² hope this helps ♥

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AP®︎ Calculus AB (2017 edition)

Course: AP®︎ Calculus AB (2017 edition) > Unit 11

Lesson 6: Volume: disc method

Disc method worksheet

Google Classroom

Gain some risk-free experience with applying the disc method in this worksheet, before you attempt our exercise.

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Leo Bekerman
Posted 7 years ago. Direct link to Leo Bekerman's post “For problem 6, isn't the ...”
For problem 6, isn't the radius of the disc (9 - y), not (9 - y^2)? The explanation says you can "see this from the graph" but what I see is [9 - f(x)] and f(x) = Y; therefore, r = (9 - y), right?
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- Bea
  Posted 7 years ago. Direct link to Bea's post “f(x)=√x, not y. You shoul...”
  f(x)=√x, not y. You should be integrating π∫[9-f(y)]dy. The given curve is y=√x, but if we're going to evaluate an integral using dy then our equation also has to be in terms of y. If we square both sides of y=√x, we get y²=x. So f(y)=y², and our radius r=9-f(y) is 9-y²
  
  hope this helps ♥
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Brenden Delong
Posted 6 years ago. Direct link to Brenden Delong's post “consider this problem "y=...”
consider this problem "y=4-x^2 bounded by y=0 rotated around y=4 What is the volume?"
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Liz Pulley
Posted 5 years ago. Direct link to Liz Pulley's post “why are the bounds y=0 an...”
why are the bounds y=0 and y=3.... how did you find y=3
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BreAnna
Posted 7 years ago. Direct link to BreAnna's post “For # 6, why is the radiu...”
For # 6, why is the radius of the disk (9-x) instead of (9-sqrtx) ?
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AP®︎ Calculus AB (2017 edition)

Course: AP®︎ Calculus AB (2017 edition) > Unit 11

Disc method worksheet

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

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