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
xy2y = √(2x)

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

y = √(2x)0 ≤ x ≤ 2
V =
2.Easy
xy1y = xex​

Evaluate I = ∫₀1 x·ex dx.

∫₀1 x·ex dx
I =
3.Medium
xy01

Evaluate I = ∫01 ex dx.

f(x) = ex[0, 1]
I =
4.Medium
xy12

Evaluate I = ∫12 4/x dx.

f(x) = 4/x[1, 2]
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
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. V = 12.57
  2. 2. I = 1
  3. 3. I = 1.718
  4. 4. I = 2.773
  5. 5. A = 1.333
  6. 6. A = 10.67

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