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
xy−12

Evaluate I = ∫−12 (−x3 − 6x + 8) dx.

f(x) = −x3 − 6x + 8[−1, 2]
I =
2.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 =
3.Medium
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 =
4.Medium
xy1y = √(2x)

The region under y = √(2x) from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(2x)0 ≤ x ≤ 1
V =
5.Hard
xy−11

Find the area A of the region between the parabola y = 1 − x² and the x-axis.

y = 1 − x²
A =
6.Hard
xy1y = x²eˣ

Evaluate I = ∫₀1 x²·eˣ dx.

∫₀1 x²eˣ dx
I =

Answer key

  1. 1. I = 11.25
  2. 2. V = 100.5
  3. 3. V = 16.76
  4. 4. V = 3.142
  5. 5. A = 1.333
  6. 6. I = 0.7183

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