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−11

Evaluate I = ∫−11 (−2x3 − 6x + 1) dx.

f(x) = −2x3 − 6x + 1[−1, 1]
I =
2.Easy
xy−20

Evaluate I = ∫−20 (−3x2 + 5x + 4) dx.

f(x) = −3x2 + 5x + 4[−2, 0]
I =
3.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)3 dx.

f(x) = 2x·(x² + 1)3[0, 2]
I =
4.Medium
xy4y = 0.5x

The region under y = 0.5x from x = 0 to x = 4 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 4
V =
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 = x2​y = 2x

Find the area A of the region enclosed by y = x2 and y = 2x.

y = x2y = 2x
A =

Answer key

  1. 1. I = 2
  2. 2. I = −10
  3. 3. I = 156
  4. 4. V = 16.76
  5. 5. A = 1.333
  6. 6. A = 1.333

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