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
xy0.5y = xe−x​

Evaluate I = ∫₀0.5 x·e−x dx.

∫₀0.5 x·e−x dx
I =
2.Easy
xy14

Evaluate I = ∫14 (3x3 − 3x − 4) dx.

f(x) = 3x3 − 3x − 4[1, 4]
I =
3.Medium
xyπy = x·sin x

Evaluate I = ∫₀π x·sin x dx (x in radians).

∫₀π x·sin x dx
I =
4.Medium
xy15y = x ln x

Evaluate I = ∫₁5 x·ln x dx.

∫₁5 x ln x dx
I =
5.Hard
xyy = 0.5x2​y = 3x

Find the area A of the region enclosed by y = 0.5x2 and y = 3x.

y = 0.5x2y = 3x
A =
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 = 0.0902
  2. 2. I = 156.8
  3. 3. I = 3.142
  4. 4. I = 14.12
  5. 5. A = 18
  6. 6. V = 407.2

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