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 = x

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

y = x0 ≤ x ≤ 2
V =
2.Easy
xy03

Evaluate I = ∫03 (−4x3 − 3x + 6) dx.

f(x) = −4x3 − 3x + 6[0, 3]
I =
3.Medium
xy3y = 0.5x

The region under y = 0.5x from x = 0 to x = 3 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 3
V =
4.Medium
xy11.5y = x ln x

Evaluate I = ∫₁1.5 x·ln x dx.

∫₁1.5 x ln x dx
I =
5.Hard
xy2y = 2xy = x²

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

y = 2xy = x²
V =
6.Hard
xy1.5y = 3xy = 2x²

The region between the line y = 3x and the parabola y = 2x² is rotated about the x-axis. Find the volume V of the solid.

y = 3xy = 2x²
V =

Answer key

  1. 1. V = 8.378
  2. 2. I = −76.5
  3. 3. V = 7.069
  4. 4. I = 0.1436
  5. 5. V = 13.4
  6. 6. V = 12.72

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