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
xy−20

Evaluate I = ∫−20 (−4x2 − 3x + 6) dx.

f(x) = −4x2 − 3x + 6[−2, 0]
I =
2.Easy
xy3y = √(4x)

The region under y = √(4x) from x = 0 to x = 3 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(4x)0 ≤ x ≤ 3
V =
3.Medium
xy01

Evaluate I = ∫01 2x·(x² + 1)2 dx.

f(x) = 2x·(x² + 1)2[0, 1]
I =
4.Medium
xy4y = 0.5x

The region under y = 0.5x from x = 0 to x = 4 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 4
V =
5.Hard
xy−33

Find the area A of the region between the parabola y = 9 − x² and the x-axis.

y = 9 − x²
A =
6.Hard
xy3y = 3xy = x²

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

y = 3xy = x²
V =

Answer key

  1. 1. I = 7.333
  2. 2. V = 56.55
  3. 3. I = 2.333
  4. 4. V = 16.76
  5. 5. A = 36
  6. 6. V = 101.8

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