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
xy4y = 0.5x

The region under y = 0.5x from x = 0 to x = 4 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 4
V =
3.Medium
xy16y = x ln x

Evaluate I = ∫₁6 x·ln x dx.

∫₁6 x ln x dx
I =
4.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)1 dx.

f(x) = 2x·(x² + 1)1[0, 2]
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
xyy = x2​y = 4x

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

y = x2y = 4x
A =

Answer key

  1. 1. V = 25.13
  2. 2. V = 16.76
  3. 3. I = 23.5
  4. 4. I = 12
  5. 5. A = 4.5
  6. 6. A = 10.67

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