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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
xy−10

Evaluate I = ∫−10 (−x2 − 3x − 3) dx.

f(x) = −x2 − 3x − 3[−1, 0]
I =
2.Easy
xy2y = 0.5x

The region under y = 0.5x from x = 0 to x = 2 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 2
V =
3.Medium
xy03

Evaluate I = ∫03 ex dx.

f(x) = ex[0, 3]
I =
4.Medium
xy02

Evaluate I = ∫02 e−0.5x dx.

f(x) = e−0.5x[0, 2]
I =
5.Hard
xy−22

Find the area A of the region between the parabola y = 4 − x² and the x-axis.

y = 4 − x²
A =
6.Hard
xy1y = 2xy = 2x²

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

y = 2xy = 2x²
V =

Answer key

  1. 1. I = −1.833
  2. 2. V = 2.094
  3. 3. I = 19.09
  4. 4. I = 1.264
  5. 5. A = 10.67
  6. 6. V = 1.676

Full step-by-step solutions: practise this topic on examproblems.com.