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
xy−2−1

Evaluate I = ∫−2−1 (4x2 + 5x − 5) dx.

f(x) = 4x2 + 5x − 5[−2, −1]
I =
2.Easy
xy−2−1

Evaluate I = ∫−2−1 (−4x3 + 5x + 1) dx.

f(x) = −4x3 + 5x + 1[−2, −1]
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
xy02

Evaluate I = ∫02 e−x dx.

f(x) = e−x[0, 2]
I =
5.Hard
xy2y = x²eˣ

Evaluate I = ∫₀2 x²·eˣ dx.

∫₀2 x²eˣ dx
I =
6.Hard
xy3y = 6xy = 2x²

The region between the line y = 6x and the parabola y = 2x² is rotated about the x-axis. Find the volume V of the solid.

y = 6xy = 2x²
V =

Answer key

  1. 1. I = −3.167
  2. 2. I = 8.5
  3. 3. V = 28.27
  4. 4. I = 0.8647
  5. 5. I = 12.78
  6. 6. V = 407.2

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