Calculus Area and Revolution

Write the integral that would be used to find the area bounded by y = x² + 1, y = x - 2, x = -2 and x = 2.

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Write the integral that would be used to find the area of the region bounded by x = 1, y = √x and y = -x + 6.

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Write the integral that can be used to find the region bounded by x = -3y² + 4 and x = y³.

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Find the area of the region bounded by the graphs of y = x² and y = 4x.

• 32/3

• 64/3

• 32

• 64

• 32/5

Write the integral that would be used to find the volume of the solid obtained by revolving the region bounded by x = y² - 4, x = 0 and y = 0 about the y-axis.

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NO CALCULATOR: Find the volume of the solid generated by revolving the area bounded by y = x² and the x-axis from [0, 2] around the x-axis. 

• 8π/3
• 32π/5
• 108π/5
• 16π/3

NO CALCULATOR: 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

What is the volume of the solid generated by rotating the region enclosed by y = sin(x) and the x-axis, from x = 0 to x = π about the x-axis?

• π²

• π²/2

• 4π²

• π/2