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
xy4y = √(x)

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

y = √(x)0 ≤ x ≤ 4
V =
2.Easy
xy3y = 2x

The region under y = 2x from x = 0 to x = 3 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 2x0 ≤ x ≤ 3
V =
3.Medium
xy2y = x·sin x

Evaluate I = ∫₀2 x·sin x dx (x in radians).

∫₀2 x·sin x dx
I =
4.Medium
xy03

Evaluate I = ∫03 e2x dx.

f(x) = e2x[0, 3]
I =
5.Hard
xy1y = x²eˣ

Evaluate I = ∫₀1 x²·eˣ dx.

∫₀1 x²eˣ dx
I =
6.Hard
xyy = 2x2​y = 4x

Find the area A of the region enclosed by y = 2x2 and y = 4x.

y = 2x2y = 4x
A =

Answer key

  1. 1. V = 25.13
  2. 2. V = 113.1
  3. 3. I = 1.742
  4. 4. I = 201.2
  5. 5. I = 0.7183
  6. 6. A = 2.667

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