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
xy1y = x

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

y = x0 ≤ x ≤ 1
V =
2.Easy
xy−20

Evaluate I = ∫−20 (−2x3 + x + 2) dx.

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

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

y = x0 ≤ x ≤ 3
V =
4.Medium
xy13y = x ln x

Evaluate I = ∫₁3 x·ln x dx.

∫₁3 x ln x dx
I =
5.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 =
6.Hard
xy1y = x²eˣ

Evaluate I = ∫₀1 x²·eˣ dx.

∫₀1 x²eˣ dx
I =

Answer key

  1. 1. V = 1.047
  2. 2. I = 10
  3. 3. V = 28.27
  4. 4. I = 2.944
  5. 5. V = 163.6
  6. 6. I = 0.7183

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