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
xy2y = 2x

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

y = 2x0 ≤ x ≤ 2
V =
2.Easy
xy2y = xe−x​

Evaluate I = ∫₀2 x·e−x dx.

∫₀2 x·e−x dx
I =
3.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)3 dx.

f(x) = 2x·(x² + 1)3[0, 2]
I =
4.Medium
xy14y = x ln x

Evaluate I = ∫₁4 x·ln x dx.

∫₁4 x ln x dx
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
xy2y = xy = 0.5x²

The region between the line y = x and the parabola y = 0.5x² is rotated about the x-axis. Find the volume V of the solid.

y = xy = 0.5x²
V =

Answer key

  1. 1. V = 33.51
  2. 2. I = 0.594
  3. 3. I = 156
  4. 4. I = 7.34
  5. 5. A = 10.67
  6. 6. V = 3.351

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