Disc Method: Revolving Around Other Axes - AP Calculus BC
Card 1 of 30
What change is made to the disc method when revolving around a horizontal line $y = c$?
What change is made to the disc method when revolving around a horizontal line $y = c$?
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Use $|f(x) - c|$ as radius. Distance from curve to line $y=c$ becomes the new radius.
Use $|f(x) - c|$ as radius. Distance from curve to line $y=c$ becomes the new radius.
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How is the disc method implemented for a solid of revolution about $y = b$?
How is the disc method implemented for a solid of revolution about $y = b$?
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Adjust radius: $|g(y) - b|$. Distance from curve to horizontal line $y=b$ becomes radius.
Adjust radius: $|g(y) - b|$. Distance from curve to horizontal line $y=b$ becomes radius.
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What is the effect of changing the axis of rotation to $y = c$?
What is the effect of changing the axis of rotation to $y = c$?
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Radius becomes $|f(x) - c|$. Shift from x-axis changes radius to distance from line.
Radius becomes $|f(x) - c|$. Shift from x-axis changes radius to distance from line.
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How do you adjust the disc method formula for revolving around the y-axis?
How do you adjust the disc method formula for revolving around the y-axis?
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Use $x = f(y)$ instead of $y = f(x)$. Switch to integrating with respect to $y$ and use horizontal cross-sections.
Use $x = f(y)$ instead of $y = f(x)$. Switch to integrating with respect to $y$ and use horizontal cross-sections.
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What is the role of the function $g(y)$ in the disc method when using the y-axis?
What is the role of the function $g(y)$ in the disc method when using the y-axis?
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It defines the radius for integration. Function $g(y)$ gives horizontal distance from y-axis.
It defines the radius for integration. Function $g(y)$ gives horizontal distance from y-axis.
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What adjustment is made to the disc method for a non-axis vertical line?
What adjustment is made to the disc method for a non-axis vertical line?
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Adjust radius: $|g(y) - \text{line}|$. Distance from function to vertical line becomes radius.
Adjust radius: $|g(y) - \text{line}|$. Distance from function to vertical line becomes radius.
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How does the function $f(x)$ affect the volume when using the disc method?
How does the function $f(x)$ affect the volume when using the disc method?
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It determines the radius. Function values determine cross-sectional radii at each point.
It determines the radius. Function values determine cross-sectional radii at each point.
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Describe how to use the disc method when revolving around a non-axis line.
Describe how to use the disc method when revolving around a non-axis line.
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Adjust radius as $|f(x) - \text{line}|$. The distance from curve to the line becomes the radius.
Adjust radius as $|f(x) - \text{line}|$. The distance from curve to the line becomes the radius.
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What is the role of the limits of integration in the disc method?
What is the role of the limits of integration in the disc method?
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They define the bounds of integration. Limits specify the interval over which to integrate.
They define the bounds of integration. Limits specify the interval over which to integrate.
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What is the effect of changing the axis of rotation to $x = c$?
What is the effect of changing the axis of rotation to $x = c$?
Tap to reveal answer
Radius becomes $|g(y) - c|$. Shift from y-axis changes radius to distance from line.
Radius becomes $|g(y) - c|$. Shift from y-axis changes radius to distance from line.
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How do you determine the limits of integration for revolving around the y-axis?
How do you determine the limits of integration for revolving around the y-axis?
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Use the interval $[c, d]$ of $y$. Integration bounds match the range of the function.
Use the interval $[c, d]$ of $y$. Integration bounds match the range of the function.
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What change is made to the disc method when revolving around a vertical line $x = c$?
What change is made to the disc method when revolving around a vertical line $x = c$?
Tap to reveal answer
Use $|g(y) - c|$ as radius. Distance from curve to line $x=c$ becomes the new radius.
Use $|g(y) - c|$ as radius. Distance from curve to line $x=c$ becomes the new radius.
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Identify the expression for the radius in the disc method revolving around the x-axis.
Identify the expression for the radius in the disc method revolving around the x-axis.
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Radius = $f(x)$. The function value gives the distance from x-axis to curve.
Radius = $f(x)$. The function value gives the distance from x-axis to curve.
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How do you determine the limits of integration for revolving around the x-axis?
How do you determine the limits of integration for revolving around the x-axis?
Tap to reveal answer
Use the interval $[a, b]$ of $x$. Integration bounds match the domain of the function.
Use the interval $[a, b]$ of $x$. Integration bounds match the domain of the function.
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What adjustment is made to the disc method for a non-axis horizontal line?
What adjustment is made to the disc method for a non-axis horizontal line?
Tap to reveal answer
Adjust radius: $|f(x) - \text{line}|$. Distance from function to horizontal line becomes radius.
Adjust radius: $|f(x) - \text{line}|$. Distance from function to horizontal line becomes radius.
← Didn't Know|Knew It →
Identify the expression for the radius in the disc method revolving around the y-axis.
Identify the expression for the radius in the disc method revolving around the y-axis.
Tap to reveal answer
Radius = $g(y)$. The function $g(y)$ gives distance from y-axis to curve.
Radius = $g(y)$. The function $g(y)$ gives distance from y-axis to curve.
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Describe how to use the disc method when revolving around a non-axis line.
Describe how to use the disc method when revolving around a non-axis line.
Tap to reveal answer
Adjust radius as $|f(x) - \text{line}|$. The distance from curve to the line becomes the radius.
Adjust radius as $|f(x) - \text{line}|$. The distance from curve to the line becomes the radius.
← Didn't Know|Knew It →
What adjustment is made to the disc method for a non-axis horizontal line?
What adjustment is made to the disc method for a non-axis horizontal line?
Tap to reveal answer
Adjust radius: $|f(x) - \text{line}|$. Distance from function to horizontal line becomes radius.
Adjust radius: $|f(x) - \text{line}|$. Distance from function to horizontal line becomes radius.
← Didn't Know|Knew It →
What is the effect of changing the axis of rotation to $x = c$?
What is the effect of changing the axis of rotation to $x = c$?
Tap to reveal answer
Radius becomes $|g(y) - c|$. Shift from y-axis changes radius to distance from line.
Radius becomes $|g(y) - c|$. Shift from y-axis changes radius to distance from line.
← Didn't Know|Knew It →
What is the role of the limits of integration in the disc method?
What is the role of the limits of integration in the disc method?
Tap to reveal answer
They define the bounds of integration. Limits specify the interval over which to integrate.
They define the bounds of integration. Limits specify the interval over which to integrate.
← Didn't Know|Knew It →
What change is made to the disc method when revolving around a horizontal line $y = c$?
What change is made to the disc method when revolving around a horizontal line $y = c$?
Tap to reveal answer
Use $|f(x) - c|$ as radius. Distance from curve to line $y=c$ becomes the new radius.
Use $|f(x) - c|$ as radius. Distance from curve to line $y=c$ becomes the new radius.
← Didn't Know|Knew It →
How does the function $f(x)$ affect the volume when using the disc method?
How does the function $f(x)$ affect the volume when using the disc method?
Tap to reveal answer
It determines the radius. Function values determine cross-sectional radii at each point.
It determines the radius. Function values determine cross-sectional radii at each point.
← Didn't Know|Knew It →
What adjustment is made to the disc method for a non-axis vertical line?
What adjustment is made to the disc method for a non-axis vertical line?
Tap to reveal answer
Adjust radius: $|g(y) - \text{line}|$. Distance from function to vertical line becomes radius.
Adjust radius: $|g(y) - \text{line}|$. Distance from function to vertical line becomes radius.
← Didn't Know|Knew It →
Identify the expression for the radius in the disc method revolving around the y-axis.
Identify the expression for the radius in the disc method revolving around the y-axis.
Tap to reveal answer
Radius = $g(y)$. The function $g(y)$ gives distance from y-axis to curve.
Radius = $g(y)$. The function $g(y)$ gives distance from y-axis to curve.
← Didn't Know|Knew It →
How do you determine the limits of integration for revolving around the x-axis?
How do you determine the limits of integration for revolving around the x-axis?
Tap to reveal answer
Use the interval $[a, b]$ of $x$. Integration bounds match the domain of the function.
Use the interval $[a, b]$ of $x$. Integration bounds match the domain of the function.
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How is the disc method implemented for a solid of revolution about $y = b$?
How is the disc method implemented for a solid of revolution about $y = b$?
Tap to reveal answer
Adjust radius: $|g(y) - b|$. Distance from curve to horizontal line $y=b$ becomes radius.
Adjust radius: $|g(y) - b|$. Distance from curve to horizontal line $y=b$ becomes radius.
← Didn't Know|Knew It →
How do you adjust the disc method formula for revolving around the y-axis?
How do you adjust the disc method formula for revolving around the y-axis?
Tap to reveal answer
Use $x = f(y)$ instead of $y = f(x)$. Switch to integrating with respect to $y$ and use horizontal cross-sections.
Use $x = f(y)$ instead of $y = f(x)$. Switch to integrating with respect to $y$ and use horizontal cross-sections.
← Didn't Know|Knew It →
Identify the expression for the radius in the disc method revolving around the x-axis.
Identify the expression for the radius in the disc method revolving around the x-axis.
Tap to reveal answer
Radius = $f(x)$. The function value gives the distance from x-axis to curve.
Radius = $f(x)$. The function value gives the distance from x-axis to curve.
← Didn't Know|Knew It →
What change is made to the disc method when revolving around a vertical line $x = c$?
What change is made to the disc method when revolving around a vertical line $x = c$?
Tap to reveal answer
Use $|g(y) - c|$ as radius. Distance from curve to line $x=c$ becomes the new radius.
Use $|g(y) - c|$ as radius. Distance from curve to line $x=c$ becomes the new radius.
← Didn't Know|Knew It →
How do you determine the limits of integration for revolving around the y-axis?
How do you determine the limits of integration for revolving around the y-axis?
Tap to reveal answer
Use the interval $[c, d]$ of $y$. Integration bounds match the range of the function.
Use the interval $[c, d]$ of $y$. Integration bounds match the range of the function.
← Didn't Know|Knew It →