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.

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1.Easy
xy−12

Evaluate I = ∫−12 (x3 − x − 5) dx.

f(x) = x3 − x − 5[−1, 2]
I =
2.Easy
xy01

Evaluate I = ∫01 (−4x2 + 2x) dx.

f(x) = −4x2 + 2x[0, 1]
I =
3.Medium
xy01

Evaluate I = ∫01 e−x dx.

f(x) = e−x[0, 1]
I =
4.Medium
xy01

Evaluate I = ∫01 2x·(x² + 1)1 dx.

f(x) = 2x·(x² + 1)1[0, 1]
I =
5.Hard
xyy = 2x2​y = 3x

Find the area A of the region enclosed by y = 2x2 and y = 3x.

y = 2x2y = 3x
A =
6.Hard
xy−33

Find the area A of the region between the parabola y = 9 − x² and the x-axis.

y = 9 − x²
A =

Answer key

  1. 1. I = −12.75
  2. 2. I = −0.3333
  3. 3. I = 0.6321
  4. 4. I = 1.5
  5. 5. A = 1.125
  6. 6. A = 36

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