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−12

Evaluate I = ∫−12 (−3x3 + 2x + 3) dx.

f(x) = −3x3 + 2x + 3[−1, 2]
I =
2.Easy
xy03

Evaluate I = ∫03 (−2x3 − 6x + 1) dx.

f(x) = −2x3 − 6x + 1[0, 3]
I =
3.Medium
xy2y = √(4x)

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

y = √(4x)0 ≤ x ≤ 2
V =
4.Medium
xy02

Evaluate I = ∫02 e−x dx.

f(x) = e−x[0, 2]
I =
5.Hard
xy−22

Find the area A of the region between the parabola y = 4 − x² and the x-axis.

y = 4 − x²
A =
6.Hard
xy1y = x²eˣ

Evaluate I = ∫₀1 x²·eˣ dx.

∫₀1 x²eˣ dx
I =

Answer key

  1. 1. I = 0.75
  2. 2. I = −64.5
  3. 3. V = 25.13
  4. 4. I = 0.8647
  5. 5. A = 10.67
  6. 6. I = 0.7183

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