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
xy4y = √(4x)

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

y = √(4x)0 ≤ x ≤ 4
V =
2.Easy
xy02

Evaluate I = ∫02 (x2 − 2) dx.

f(x) = x2 − 2[0, 2]
I =
3.Medium
xy01

Evaluate I = ∫01 2x·(x² + 1)1 dx.

f(x) = 2x·(x² + 1)1[0, 1]
I =
4.Medium
xy2y = x·cos x

Evaluate I = ∫₀2 x·cos x dx (x in radians).

∫₀2 x·cos x dx
I =
5.Hard
xy−11

Find the area A of the region between the parabola y = 1 − x² and the x-axis.

y = 1 − x²
A =
6.Hard
xy3y = x²eˣ

Evaluate I = ∫₀3 x²·eˣ dx.

∫₀3 x²eˣ dx
I =

Answer key

  1. 1. V = 100.5
  2. 2. I = −1.333
  3. 3. I = 1.5
  4. 4. I = 0.4024
  5. 5. A = 1.333
  6. 6. I = 98.43

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