Calculus Revolved Find Volume

If the region enclosed by these functions are revolved around the y axis, would one use a washer or disk?

• washer

• disk

Select the integral that would find the volume of the region revolving around the given axis.

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Select the integral that would find the volume of the region revolving around the given axis.

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The region bounded by the line y = x and y = f(x) is rotated about the line y = k. Choose the correct representations of R and r

• R = k + f(x)

• R = k − f(x)

• r = k + x

• r = k − x

Find the volume of the solid generated by revolving the area bounded by y = x² and the x-axis from [0, 2] around the y-axis. 

• 8π

• 6π

• 2π

• 0

Determine the volume of the region bounded by y = x² - 2x and y = x that is rotated about y = 4.

• 5.4

• 30.6

• 96.133

• 108.332

Find the volume of the solid of revolution obtained by rotating the region in bounded by y = x³ + 1, x = 1 and y = 1 about the y-axis.

• 11π/3

• 4π/13

• 3π/7

• 2π/5

What integral would allow you to find the volume of the region bounded by y = 2x² and y = 8 around the line y = 11. 

• Bounds: [0, 2]; π ∫(4x⁴ - 8)dx

• Bounds: [0, 2]; π ∫((11 - 2x²)² - 9)dx

• Bounds: [-2, 2]; π ∫((11 - 2x²)² - 9)dx

• Bounds: [-2, 2]; π ∫(4x⁴ - 8)dx

A champagne flute is designed by rotating the curve from to about the x-axis. What is the capacity of the flute?

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Find the volume of the solid generated by revolving the area bounded by y = x² and the x-axis from [0, 2] around the y-axis. 

• 8π

• 6π

• 2π

• 0