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
xy2y = xex​

Evaluate I = ∫₀2 x·ex dx.

∫₀2 x·ex dx
I =
2.Easy
xy1y = xe2x​

Evaluate I = ∫₀1 x·e2x dx.

∫₀1 x·e2x dx
I =
3.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)2 dx.

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

Evaluate I = ∫01 2x·(x² + 1)2 dx.

f(x) = 2x·(x² + 1)2[0, 1]
I =
5.Hard
xyy = 2x2​y = 4x

Find the area A of the region enclosed by y = 2x2 and y = 4x.

y = 2x2y = 4x
A =
6.Hard
xy3y = x²eˣ

Evaluate I = ∫₀3 x²·eˣ dx.

∫₀3 x²eˣ dx
I =

Answer key

  1. 1. I = 8.389
  2. 2. I = 2.097
  3. 3. I = 41.33
  4. 4. I = 2.333
  5. 5. A = 2.667
  6. 6. I = 98.43

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