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 = xe−x​

Evaluate I = ∫₀3 x·e−x dx.

∫₀3 x·e−x dx
I =
2.Easy
xy1.5y = xex​

Evaluate I = ∫₀1.5 x·ex dx.

∫₀1.5 x·ex dx
I =
3.Medium
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 =
4.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)3 dx.

f(x) = 2x·(x² + 1)3[0, 2]
I =
5.Hard
xyy = x2​y = 4x

Find the area A of the region enclosed by y = x2 and y = 4x.

y = x2y = 4x
A =
6.Hard
xy−22

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

y = 4 − x²
A =

Answer key

  1. 1. I = 0.8009
  2. 2. I = 3.241
  3. 3. V = 28.27
  4. 4. I = 156
  5. 5. A = 10.67
  6. 6. A = 10.67

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