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
xy14

Evaluate I = ∫14 (−3x3 − 4x + 3) dx.

f(x) = −3x3 − 4x + 3[1, 4]
I =
3.Medium
xy03

Evaluate I = ∫03 ex dx.

f(x) = ex[0, 3]
I =
4.Medium
xy1y = x·sin x

Evaluate I = ∫₀1 x·sin x dx (x in radians).

∫₀1 x·sin x dx
I =
5.Hard
xy1.5y = x²eˣ

Evaluate I = ∫₀1.5 x²·eˣ dx.

∫₀1.5 x²eˣ dx
I =
6.Hard
xy1y = x²eˣ

Evaluate I = ∫₀1 x²·eˣ dx.

∫₀1 x²eˣ dx
I =

Answer key

  1. 1. V = 33.51
  2. 2. I = −212.3
  3. 3. I = 19.09
  4. 4. I = 0.3012
  5. 5. I = 3.602
  6. 6. I = 0.7183

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