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 = 2x

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

y = 2x0 ≤ x ≤ 2
V =
2.Easy
xy3y = xex/2​

Evaluate I = ∫₀3 x·ex/2 dx.

∫₀3 x·ex/2 dx
I =
3.Medium
xyπ/3y = x·cos x

Evaluate I = ∫₀π/3 x·cos x dx (x in radians).

∫₀π/3 x·cos x dx
I =
4.Medium
xy12.5y = x ln x

Evaluate I = ∫₁2.5 x·ln x dx.

∫₁2.5 x ln x dx
I =
5.Hard
xy1.5y = x²eˣ

Evaluate I = ∫₀1.5 x²·eˣ dx.

∫₀1.5 x²eˣ dx
I =
6.Hard
xy−33

Find the area A of the region between the parabola y = 9 − x² and the x-axis.

y = 9 − x²
A =

Answer key

  1. 1. V = 33.51
  2. 2. I = 12.96
  3. 3. I = 0.4069
  4. 4. I = 1.551
  5. 5. I = 3.602
  6. 6. A = 36

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