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−21

Evaluate I = ∫−21 (−4x2 − 5x − 2) dx.

f(x) = −4x2 − 5x − 2[−2, 1]
I =
2.Easy
xy1y = x

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

y = x0 ≤ x ≤ 1
V =
3.Medium
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 =
4.Medium
xy03

Evaluate I = ∫03 ex dx.

f(x) = ex[0, 3]
I =
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
xy1y = xy = x²

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

y = xy = x²
V =

Answer key

  1. 1. I = −10.5
  2. 2. V = 1.047
  3. 3. V = 56.55
  4. 4. I = 19.09
  5. 5. A = 36
  6. 6. V = 0.4189

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