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 = 0.5x

The region under y = 0.5x from x = 0 to x = 2 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 2
V =
2.Easy
xy2.5y = xe2x​

Evaluate I = ∫₀2.5 x·e2x dx.

∫₀2.5 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
xy13

Evaluate I = ∫13 1/x dx.

f(x) = 1/x[1, 3]
I =
5.Hard
xy−22

Find the area A of the region between the parabola y = 4 − x² and the x-axis.

y = 4 − x²
A =
6.Hard
xy1.5y = x²eˣ

Evaluate I = ∫₀1.5 x²·eˣ dx.

∫₀1.5 x²eˣ dx
I =

Answer key

  1. 1. V = 2.094
  2. 2. I = 148.7
  3. 3. I = 41.33
  4. 4. I = 1.099
  5. 5. A = 10.67
  6. 6. I = 3.602

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