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−20

Evaluate I = ∫−20 (3x2 − 5x + 2) dx.

f(x) = 3x2 − 5x + 2[−2, 0]
I =
2.Easy
xy0.5y = xex/2​

Evaluate I = ∫₀0.5 x·ex/2 dx.

∫₀0.5 x·ex/2 dx
I =
3.Medium
xy4y = √(2x)

The region under y = √(2x) from x = 0 to x = 4 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(2x)0 ≤ x ≤ 4
V =
4.Medium
xy12y = x ln x

Evaluate I = ∫₁2 x·ln x dx.

∫₁2 x ln x dx
I =
5.Hard
xyy = x2​y = x

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

y = x2y = x
A =
6.Hard
xy0.5y = x²eˣ

Evaluate I = ∫₀0.5 x²·eˣ dx.

∫₀0.5 x²eˣ dx
I =

Answer key

  1. 1. I = 22
  2. 2. I = 0.1479
  3. 3. V = 50.27
  4. 4. I = 0.6363
  5. 5. A = 0.1667
  6. 6. I = 0.0609

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