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 = 3x

The region under y = 3x from x = 0 to x = 3 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 3x0 ≤ x ≤ 3
V =
2.Easy
xy3y = xe−x​

Evaluate I = ∫₀3 x·e−x dx.

∫₀3 x·e−x dx
I =
3.Medium
xy12y = x ln x

Evaluate I = ∫₁2 x·ln x dx.

∫₁2 x ln x dx
I =
4.Medium
xy4y = √(2x)

The region under y = √(2x) from x = 0 to x = 4 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(2x)0 ≤ x ≤ 4
V =
5.Hard
xy2y = x²eˣ

Evaluate I = ∫₀2 x²·eˣ dx.

∫₀2 x²eˣ dx
I =
6.Hard
xyy = 2x2​y = 2x

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

y = 2x2y = 2x
A =

Answer key

  1. 1. V = 254.5
  2. 2. I = 0.8009
  3. 3. I = 0.6363
  4. 4. V = 50.27
  5. 5. I = 12.78
  6. 6. A = 0.3333

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