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−10

Evaluate I = ∫−10 (−2x2 + 5x) dx.

f(x) = −2x2 + 5x[−1, 0]
I =
2.Easy
xy−12

Evaluate I = ∫−12 (−3x3 + 3x + 2) dx.

f(x) = −3x3 + 3x + 2[−1, 2]
I =
3.Medium
xy12

Evaluate I = ∫12 3/x dx.

f(x) = 3/x[1, 2]
I =
4.Medium
xy11.5y = x ln x

Evaluate I = ∫₁1.5 x·ln x dx.

∫₁1.5 x ln x dx
I =
5.Hard
xyy = x2​y = x

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

y = x2y = x
A =
6.Hard
xyy = 2x2​y = 3x

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

y = 2x2y = 3x
A =

Answer key

  1. 1. I = −3.167
  2. 2. I = −0.75
  3. 3. I = 2.079
  4. 4. I = 0.1436
  5. 5. A = 0.1667
  6. 6. A = 1.125

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