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
xy1y = √(x)

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

y = √(x)0 ≤ x ≤ 1
V =
2.Easy
xy01

Evaluate I = ∫01 (−x2 − x + 6) dx.

f(x) = −x2 − x + 6[0, 1]
I =
3.Medium
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 =
4.Medium
xy2y = 0.5x

The region under y = 0.5x from x = 0 to x = 2 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 2
V =
5.Hard
xy0.5y = x²eˣ

Evaluate I = ∫₀0.5 x²·eˣ dx.

∫₀0.5 x²eˣ dx
I =
6.Hard
xy2y = x²eˣ

Evaluate I = ∫₀2 x²·eˣ dx.

∫₀2 x²eˣ dx
I =

Answer key

  1. 1. V = 1.571
  2. 2. I = 5.167
  3. 3. V = 113.1
  4. 4. V = 2.094
  5. 5. I = 0.0609
  6. 6. I = 12.78

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