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 = xe−x​

Evaluate I = ∫₀2.5 x·e−x dx.

∫₀2.5 x·e−x dx
I =
2.Easy
xy−10

Evaluate I = ∫−10 (3x2 − 5x + 1) dx.

f(x) = 3x2 − 5x + 1[−1, 0]
I =
3.Medium
xy210

Evaluate I = ∫210 3/x dx.

f(x) = 3/x[2, 10]
I =
4.Medium
xy01

Evaluate I = ∫01 2x·(x² + 1)2 dx.

f(x) = 2x·(x² + 1)2[0, 1]
I =
5.Hard
xy1.5y = x²eˣ

Evaluate I = ∫₀1.5 x²·eˣ dx.

∫₀1.5 x²eˣ dx
I =
6.Hard
xy1.667y = 5xy = 3x²

The region between the line y = 5x and the parabola y = 3x² is rotated about the x-axis. Find the volume V of the solid.

y = 5xy = 3x²
V =

Answer key

  1. 1. I = 0.7127
  2. 2. I = 4.5
  3. 3. I = 4.828
  4. 4. I = 2.333
  5. 5. I = 3.602
  6. 6. V = 48.48

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