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
xy12

Evaluate I = ∫12 (3x2 + 6x + 1) dx.

f(x) = 3x2 + 6x + 1[1, 2]
I =
2.Easy
xy3y = xe2x​

Evaluate I = ∫₀3 x·e2x dx.

∫₀3 x·e2x dx
I =
3.Medium
xy01

Evaluate I = ∫01 2x·(x² + 1)3 dx.

f(x) = 2x·(x² + 1)3[0, 1]
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 = 2x2​y = x

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

y = 2x2y = x
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 = 17
  2. 2. I = 504.5
  3. 3. I = 3.75
  4. 4. I = 0.1436
  5. 5. A = 0.04167
  6. 6. A = 5.333

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