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
xy14

Evaluate I = ∫14 (x3 + x + 1) dx.

f(x) = x3 + x + 1[1, 4]
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 paraboloid).

y = √(2x)0 ≤ x ≤ 1
V =
3.Medium
xy2y = √(x)

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

y = √(x)0 ≤ x ≤ 2
V =
4.Medium
xy01

Evaluate I = ∫01 e−0.5x dx.

f(x) = e−0.5x[0, 1]
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
xyy = x2​y = 3x

Find the area A of the region enclosed by y = x2 and y = 3x.

y = x2y = 3x
A =

Answer key

  1. 1. I = 74.25
  2. 2. V = 3.142
  3. 3. V = 6.283
  4. 4. I = 0.7869
  5. 5. A = 1.333
  6. 6. A = 4.5

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