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
xy13

Evaluate I = ∫13 (2x3 − x + 3) dx.

f(x) = 2x3 − x + 3[1, 3]
I =
2.Easy
xy2y = 2x

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

y = 2x0 ≤ x ≤ 2
V =
3.Medium
xy11.5y = x ln x

Evaluate I = ∫₁1.5 x·ln x dx.

∫₁1.5 x ln x dx
I =
4.Medium
xy01

Evaluate I = ∫01 e−0.5x dx.

f(x) = e−0.5x[0, 1]
I =
5.Hard
xy0.5y = x²eˣ

Evaluate I = ∫₀0.5 x²·eˣ dx.

∫₀0.5 x²eˣ dx
I =
6.Hard
xyy = 2x2​y = 3x

Find the area A of the region enclosed by y = 2x2 and y = 3x.

y = 2x2y = 3x
A =

Answer key

  1. 1. I = 42
  2. 2. V = 33.51
  3. 3. I = 0.1436
  4. 4. I = 0.7869
  5. 5. I = 0.0609
  6. 6. A = 1.125

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