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−2−1

Evaluate I = ∫−2−1 (3x2 − 3x − 4) dx.

f(x) = 3x2 − 3x − 4[−2, −1]
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
xy1y = 0.5x

The region under y = 0.5x from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 1
V =
5.Hard
xy2y = 6xy = 3x²

The region between the line y = 6x and the parabola y = 3x² is rotated about the x-axis. Find the volume V of the solid.

y = 6xy = 3x²
V =
6.Hard
xyy = 2x2​y = 4x

Find the area A of the region enclosed by y = 2x2 and y = 4x.

y = 2x2y = 4x
A =

Answer key

  1. 1. I = 7.5
  2. 2. V = 56.55
  3. 3. I = 2.333
  4. 4. V = 0.2618
  5. 5. V = 120.6
  6. 6. A = 2.667

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