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
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 =
2.Easy
xy12

Evaluate I = ∫12 (2x2 + 4x + 8) dx.

f(x) = 2x2 + 4x + 8[1, 2]
I =
3.Medium
xy26

Evaluate I = ∫26 5/x dx.

f(x) = 5/x[2, 6]
I =
4.Medium
xy1y = x·sin x

Evaluate I = ∫₀1 x·sin x dx (x in radians).

∫₀1 x·sin x dx
I =
5.Hard
xy0.5y = x²eˣ

Evaluate I = ∫₀0.5 x²·eˣ dx.

∫₀0.5 x²eˣ dx
I =
6.Hard
xy1.5y = x²eˣ

Evaluate I = ∫₀1.5 x²·eˣ dx.

∫₀1.5 x²eˣ dx
I =

Answer key

  1. 1. V = 2.094
  2. 2. I = 18.67
  3. 3. I = 5.493
  4. 4. I = 0.3012
  5. 5. I = 0.0609
  6. 6. I = 3.602

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