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 (−3x2 − 5x) dx.

f(x) = −3x2 − 5x[−1, 2]
I =
2.Easy
xy2.5y = xe−x​

Evaluate I = ∫₀2.5 x·e−x dx.

∫₀2.5 x·e−x dx
I =
3.Medium
xy4y = x

The region under y = x from x = 0 to x = 4 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = x0 ≤ x ≤ 4
V =
4.Medium
xy13

Evaluate I = ∫13 4/x dx.

f(x) = 4/x[1, 3]
I =
5.Hard
xy2y = x²eˣ

Evaluate I = ∫₀2 x²·eˣ dx.

∫₀2 x²eˣ dx
I =
6.Hard
xy2.5y = 5xy = 2x²

The region between the line y = 5x and the parabola y = 2x² is rotated about the x-axis. Find the volume V of the solid.

y = 5xy = 2x²
V =

Answer key

  1. 1. I = −16.5
  2. 2. I = 0.7127
  3. 3. V = 67.02
  4. 4. I = 4.394
  5. 5. I = 12.78
  6. 6. V = 163.6

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