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 = x

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

y = x0 ≤ x ≤ 2
V =
2.Easy
xy3y = xe−x​

Evaluate I = ∫₀3 x·e−x dx.

∫₀3 x·e−x dx
I =
3.Medium
xy1y = √(4x)

The region under y = √(4x) from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(4x)0 ≤ x ≤ 1
V =
4.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)1 dx.

f(x) = 2x·(x² + 1)1[0, 2]
I =
5.Hard
xy2.5y = x²eˣ

Evaluate I = ∫₀2.5 x²·eˣ dx.

∫₀2.5 x²eˣ dx
I =
6.Hard
xyy = x2​y = 3x

Find the area A of the region enclosed by y = x2 and y = 3x.

y = x2y = 3x
A =

Answer key

  1. 1. V = 8.378
  2. 2. I = 0.8009
  3. 3. V = 6.283
  4. 4. I = 12
  5. 5. I = 37.59
  6. 6. A = 4.5

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