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
xy3y = √(x)

The region under y = √(x) from x = 0 to x = 3 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(x)0 ≤ x ≤ 3
V =
2.Easy
xy1.5y = xe2x​

Evaluate I = ∫₀1.5 x·e2x dx.

∫₀1.5 x·e2x dx
I =
3.Medium
xy01

Evaluate I = ∫01 e0.5x dx.

f(x) = e0.5x[0, 1]
I =
4.Medium
xy15

Evaluate I = ∫15 2/x dx.

f(x) = 2/x[1, 5]
I =
5.Hard
xyy = 2x2​y = 4x

Find the area A of the region enclosed by y = 2x2 and y = 4x.

y = 2x2y = 4x
A =
6.Hard
xy1y = 3xy = 3x²

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

y = 3xy = 3x²
V =

Answer key

  1. 1. V = 14.14
  2. 2. I = 10.29
  3. 3. I = 1.297
  4. 4. I = 3.219
  5. 5. A = 2.667
  6. 6. V = 3.77

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