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 = √(4x)

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

y = √(4x)0 ≤ x ≤ 2
V =
2.Easy
xy1y = 0.5x

The region under y = 0.5x from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 1
V =
3.Medium
xy12.5y = x ln x

Evaluate I = ∫₁2.5 x·ln x dx.

∫₁2.5 x ln x dx
I =
4.Medium
xy11.5y = x ln x

Evaluate I = ∫₁1.5 x·ln x dx.

∫₁1.5 x ln x dx
I =
5.Hard
xyy = x2​y = 3x

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

y = x2y = 3x
A =
6.Hard
xy1.5y = x²eˣ

Evaluate I = ∫₀1.5 x²·eˣ dx.

∫₀1.5 x²eˣ dx
I =

Answer key

  1. 1. V = 25.13
  2. 2. V = 0.2618
  3. 3. I = 1.551
  4. 4. I = 0.1436
  5. 5. A = 4.5
  6. 6. I = 3.602

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