Integrals worksheet with answers

Free printable Integrals worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
xy2y = √(2x)

The region under y = √(2x) from x = 0 to x = 2 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(2x)0 ≤ x ≤ 2
V =
2.Easy
xy12

Evaluate I = ∫12 (x2 + 2x + 4) dx.

f(x) = x2 + 2x + 4[1, 2]
I =
3.Medium
xy1y = √(4x)

The region under y = √(4x) from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(4x)0 ≤ x ≤ 1
V =
4.Medium
xy1y = 3x

The region under y = 3x from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 3x0 ≤ x ≤ 1
V =
5.Hard
xy1y = 2xy = 2x²

The region between the line y = 2x and the parabola y = 2x² is rotated about the x-axis. Find the volume V of the solid.

y = 2xy = 2x²
V =
6.Hard
xy2y = 4xy = 2x²

The region between the line y = 4x and the parabola y = 2x² is rotated about the x-axis. Find the volume V of the solid.

y = 4xy = 2x²
V =

Answer key

  1. 1. V = 12.57
  2. 2. I = 9.333
  3. 3. V = 6.283
  4. 4. V = 9.425
  5. 5. V = 1.676
  6. 6. V = 53.62

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