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
xy02

Evaluate I = ∫02 (−x3 + 6x + 7) dx.

f(x) = −x3 + 6x + 7[0, 2]
I =
2.Easy
xy3y = 3x

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

y = 3x0 ≤ x ≤ 3
V =
3.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)3 dx.

f(x) = 2x·(x² + 1)3[0, 2]
I =
4.Medium
xy210

Evaluate I = ∫210 3/x dx.

f(x) = 3/x[2, 10]
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
xyy = 0.5x2​y = x

Find the area A of the region enclosed by y = 0.5x2 and y = x.

y = 0.5x2y = x
A =

Answer key

  1. 1. I = 22
  2. 2. V = 254.5
  3. 3. I = 156
  4. 4. I = 4.828
  5. 5. V = 120.6
  6. 6. A = 0.6667

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