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 = √(4x)

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

y = √(4x)0 ≤ x ≤ 4
V =
2.Easy
xy−2−1

Evaluate I = ∫−2−1 (3x3 + 4x − 2) dx.

f(x) = 3x3 + 4x − 2[−2, −1]
I =
3.Medium
xy14

Evaluate I = ∫14 3/x dx.

f(x) = 3/x[1, 4]
I =
4.Medium
xy24

Evaluate I = ∫24 1/x dx.

f(x) = 1/x[2, 4]
I =
5.Hard
xy4y = 2xy = 0.5x²

The region between the line y = 2x and the parabola y = 0.5x² is rotated about the x-axis. Find the volume V of the solid.

y = 2xy = 0.5x²
V =
6.Hard
xy1.5y = 3xy = 2x²

The region between the line y = 3x and the parabola y = 2x² is rotated about the x-axis. Find the volume V of the solid.

y = 3xy = 2x²
V =

Answer key

  1. 1. V = 100.5
  2. 2. I = −19.25
  3. 3. I = 4.159
  4. 4. I = 0.6931
  5. 5. V = 107.2
  6. 6. V = 12.72

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