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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Name: ____________________   Date: ____________

1.Easy
xy1.5y = xex​

Evaluate I = ∫₀1.5 x·ex dx.

∫₀1.5 x·ex dx
I =
2.Easy
xy0.5y = xe2x​

Evaluate I = ∫₀0.5 x·e2x dx.

∫₀0.5 x·e2x dx
I =
3.Medium
xy2y = 0.5x

The region under y = 0.5x from x = 0 to x = 2 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 2
V =
4.Medium
xy15

Evaluate I = ∫15 5/x dx.

f(x) = 5/x[1, 5]
I =
5.Hard
xy−33

Find the area A of the region between the parabola y = 9 − x² and the x-axis.

y = 9 − x²
A =
6.Hard
xyy = x2​y = 3x

Find the area A of the region enclosed by y = x2 and y = 3x.

y = x2y = 3x
A =

Answer key

  1. 1. I = 3.241
  2. 2. I = 0.25
  3. 3. V = 2.094
  4. 4. I = 8.047
  5. 5. A = 36
  6. 6. A = 4.5

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