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 = x

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

y = x0 ≤ x ≤ 4
V =
2.Easy
xy12

Evaluate I = ∫12 (4x3 + 4x − 1) dx.

f(x) = 4x3 + 4x − 1[1, 2]
I =
3.Medium
xy26

Evaluate I = ∫26 2/x dx.

f(x) = 2/x[2, 6]
I =
4.Medium
xy2y = 3x

The region under y = 3x from x = 0 to x = 2 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 3x0 ≤ x ≤ 2
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
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 =

Answer key

  1. 1. V = 67.02
  2. 2. I = 20
  3. 3. I = 2.197
  4. 4. V = 75.4
  5. 5. A = 36
  6. 6. V = 13.4

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