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
xy2.5y = xe2x​

Evaluate I = ∫₀2.5 x·e2x dx.

∫₀2.5 x·e2x dx
I =
2.Easy
xy−11

Evaluate I = ∫−11 (−x2 − 2x + 4) dx.

f(x) = −x2 − 2x + 4[−1, 1]
I =
3.Medium
xy24

Evaluate I = ∫24 5/x dx.

f(x) = 5/x[2, 4]
I =
4.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)2 dx.

f(x) = 2x·(x² + 1)2[0, 2]
I =
5.Hard
xy3y = x²eˣ

Evaluate I = ∫₀3 x²·eˣ dx.

∫₀3 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 = 148.7
  2. 2. I = 7.333
  3. 3. I = 3.466
  4. 4. I = 41.33
  5. 5. I = 98.43
  6. 6. V = 163.6

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