AP Calculus Area Between Curves

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 enclosed by the lines and curves. y = -4sin(x) y = sin(2x) 0 ≤ x ≤ Π

• 6

• 8

• 9.5

• 11.25

Find the area of the region enclosed by the lines and curves.
y² = x + 8   and  x = y + 64

• 891/2

• 4913/6

• 4937/6

• 955/2

Find the area of the region enclosed by the lines and curves.
y = -4sin(x)   y = sin(2x)    0 ≤ x ≤ Π 

• 8

• 1/2

• 4

• 16

• 9/2

• 4/3

• 7/3

• 5/3

Find the area of the region enclosed by the curves.

• 5.25

• 5.75

• 10.5

• 5.583

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

The region in the first quadrant enclosed by the graphs of y=sin(x) and y=x² is revolved around the x-axis. Find the volume.

• -0.279

• 0.254

• 0.279

• -0.254

The base of a solid is the region enclosed by y=4 and y=x²/4. Cross sections perpendicular to the x-axis are squares. Find the volume of the solid.

• 51.200

• 914.667

• 85.333

• 68.267