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
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 =
2.Easy
xy3y = 0.5x

The region under y = 0.5x from x = 0 to x = 3 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 3
V =
3.Medium
xy210

Evaluate I = ∫210 3/x dx.

f(x) = 3/x[2, 10]
I =
4.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)3 dx.

f(x) = 2x·(x² + 1)3[0, 2]
I =
5.Hard
xy−11

Find the area A of the region between the parabola y = 1 − x² and the x-axis.

y = 1 − x²
A =
6.Hard
xyy = 0.5x2​y = 3x

Find the area A of the region enclosed by y = 0.5x2 and y = 3x.

y = 0.5x2y = 3x
A =

Answer key

  1. 1. V = 254.5
  2. 2. V = 7.069
  3. 3. I = 4.828
  4. 4. I = 156
  5. 5. A = 1.333
  6. 6. A = 18

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