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 = xe2x​

Evaluate I = ∫₀3 x·e2x dx.

∫₀3 x·e2x dx
I =
2.Easy
xy1y = x

The region under y = x from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = x0 ≤ x ≤ 1
V =
3.Medium
xy12

Evaluate I = ∫12 4/x dx.

f(x) = 4/x[1, 2]
I =
4.Medium
xy210

Evaluate I = ∫210 1/x dx.

f(x) = 1/x[2, 10]
I =
5.Hard
xy−11

Find the area A of the region between the parabola y = 1 − x² and the x-axis.

y = 1 − x²
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 = 504.5
  2. 2. V = 1.047
  3. 3. I = 2.773
  4. 4. I = 1.609
  5. 5. A = 1.333
  6. 6. A = 36

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