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
xy3y = √(x)

The region under y = √(x) from x = 0 to x = 3 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(x)0 ≤ x ≤ 3
V =
2.Easy
xy3y = xe2x​

Evaluate I = ∫₀3 x·e2x dx.

∫₀3 x·e2x dx
I =
3.Medium
xy15y = x ln x

Evaluate I = ∫₁5 x·ln x dx.

∫₁5 x ln x dx
I =
4.Medium
xy03

Evaluate I = ∫03 e−0.5x dx.

f(x) = e−0.5x[0, 3]
I =
5.Hard
xy1.5y = x²eˣ

Evaluate I = ∫₀1.5 x²·eˣ dx.

∫₀1.5 x²eˣ dx
I =
6.Hard
xy2y = x²eˣ

Evaluate I = ∫₀2 x²·eˣ dx.

∫₀2 x²eˣ dx
I =

Answer key

  1. 1. V = 14.14
  2. 2. I = 504.5
  3. 3. I = 14.12
  4. 4. I = 1.554
  5. 5. I = 3.602
  6. 6. I = 12.78

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