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
xy3y = xe−x​

Evaluate I = ∫₀3 x·e−x dx.

∫₀3 x·e−x dx
I =
2.Easy
xy14

Evaluate I = ∫14 (x3 − x + 5) dx.

f(x) = x3 − x + 5[1, 4]
I =
3.Medium
xy03

Evaluate I = ∫03 e−x dx.

f(x) = e−x[0, 3]
I =
4.Medium
xy15

Evaluate I = ∫15 5/x dx.

f(x) = 5/x[1, 5]
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 = 0.8009
  2. 2. I = 71.25
  3. 3. I = 0.9502
  4. 4. I = 8.047
  5. 5. A = 0.04167
  6. 6. A = 5.333

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