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
xy13

Evaluate I = ∫13 (−x2 + x + 2) dx.

f(x) = −x2 + x + 2[1, 3]
I =
2.Easy
xy12

Evaluate I = ∫12 (−4x3 + x − 1) dx.

f(x) = −4x3 + x − 1[1, 2]
I =
3.Medium
xyπy = x·cos x

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

∫₀π x·cos x dx
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
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
xyy = 0.5x2​y = 2x

Find the area A of the region enclosed by y = 0.5x2 and y = 2x.

y = 0.5x2y = 2x
A =

Answer key

  1. 1. I = −0.6667
  2. 2. I = −14.5
  3. 3. I = −2
  4. 4. I = 0.3012
  5. 5. A = 10.67
  6. 6. A = 5.333

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