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
xy02

Evaluate I = ∫02 (−x2 − 5x + 2) dx.

f(x) = −x2 − 5x + 2[0, 2]
I =
2.Easy
xy−20

Evaluate I = ∫−20 (−4x3 − x + 8) dx.

f(x) = −4x3 − x + 8[−2, 0]
I =
3.Medium
xy1y = 2x

The region under y = 2x from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 2x0 ≤ x ≤ 1
V =
4.Medium
xy12

Evaluate I = ∫12 1/x dx.

f(x) = 1/x[1, 2]
I =
5.Hard
xyy = 0.5x2​y = 2x

Find the area A of the region enclosed by y = 0.5x2 and y = 2x.

y = 0.5x2y = 2x
A =
6.Hard
xy1y = x²eˣ

Evaluate I = ∫₀1 x²·eˣ dx.

∫₀1 x²eˣ dx
I =

Answer key

  1. 1. I = −8.667
  2. 2. I = 34
  3. 3. V = 4.189
  4. 4. I = 0.6931
  5. 5. A = 5.333
  6. 6. I = 0.7183

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