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
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 =
2.Easy
xy−10

Evaluate I = ∫−10 (4x2 − 3x + 7) dx.

f(x) = 4x2 − 3x + 7[−1, 0]
I =
3.Medium
xy02

Evaluate I = ∫02 e−x dx.

f(x) = e−x[0, 2]
I =
4.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)3 dx.

f(x) = 2x·(x² + 1)3[0, 2]
I =
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
xy2.5y = 5xy = 2x²

The region between the line y = 5x and the parabola y = 2x² is rotated about the x-axis. Find the volume V of the solid.

y = 5xy = 2x²
V =

Answer key

  1. 1. V = 16.76
  2. 2. I = 9.833
  3. 3. I = 0.8647
  4. 4. I = 156
  5. 5. V = 120.6
  6. 6. V = 163.6

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