Applications of Area and Volume

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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 would be used to find the area bounded by the graphs of x - y = 2, y = 8 and x = y^2/3.

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Find the area of the region bounded by the equations y = x² + 1 and y = 5.

• 32/3

• 64

• 32

• 64/3

• 16

Write the integral that would be used to find the volume of the region bounded by x = -1, x = 2, y = 0 and y = 1/2x² + 2.

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Write the integral that would be used to find the volume of the solid generated when the region bounded by the x-axis, the y-axis and 2x + y = 6 is revolved about the x-axis.

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• A cone of base radius r and height [AB]

• A cone of base radius r and height h

• A cone of base radius h and height r

• None of the above