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
xy4y = √(x)

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

y = √(x)0 ≤ x ≤ 4
V =
2.Easy
xy4y = √(2x)

The region under y = √(2x) from x = 0 to x = 4 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(2x)0 ≤ x ≤ 4
V =
3.Medium
xy01

Evaluate I = ∫01 ex dx.

f(x) = ex[0, 1]
I =
4.Medium
xy02

Evaluate I = ∫02 e−x dx.

f(x) = e−x[0, 2]
I =
5.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 =
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. V = 25.13
  2. 2. V = 50.27
  3. 3. I = 1.718
  4. 4. I = 0.8647
  5. 5. V = 3.351
  6. 6. A = 1.333

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