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−2−1

Evaluate I = ∫−2−1 (3x2 + 3x + 5) dx.

f(x) = 3x2 + 3x + 5[−2, −1]
I =
2.Easy
xy1y = 2x

The region under y = 2x from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 2x0 ≤ x ≤ 1
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
xy1y = x·cos x

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

∫₀1 x·cos x dx
I =
5.Hard
xy2.5y = x²eˣ

Evaluate I = ∫₀2.5 x²·eˣ dx.

∫₀2.5 x²eˣ dx
I =
6.Hard
xyy = x2​y = 2x

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

y = x2y = 2x
A =

Answer key

  1. 1. I = 7.5
  2. 2. V = 4.189
  3. 3. I = 0.1436
  4. 4. I = 0.3818
  5. 5. I = 37.59
  6. 6. A = 1.333

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