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 = √(2x)

The region under y = √(2x) from x = 0 to x = 3 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(2x)0 ≤ x ≤ 3
V =
2.Easy
xy02

Evaluate I = ∫02 (2x3 + 4x − 5) dx.

f(x) = 2x3 + 4x − 5[0, 2]
I =
3.Medium
xy13

Evaluate I = ∫13 4/x dx.

f(x) = 4/x[1, 3]
I =
4.Medium
xy1y = x·cos x

Evaluate I = ∫₀1 x·cos x dx (x in radians).

∫₀1 x·cos x dx
I =
5.Hard
xy1.5y = x²eˣ

Evaluate I = ∫₀1.5 x²·eˣ dx.

∫₀1.5 x²eˣ dx
I =
6.Hard
xy−11

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

y = 1 − x²
A =

Answer key

  1. 1. V = 28.27
  2. 2. I = 6
  3. 3. I = 4.394
  4. 4. I = 0.3818
  5. 5. I = 3.602
  6. 6. A = 1.333

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