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
xy13

Evaluate I = ∫13 (2x2 + 5x − 1) dx.

f(x) = 2x2 + 5x − 1[1, 3]
I =
2.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 =
3.Medium
xy14

Evaluate I = ∫14 2/x dx.

f(x) = 2/x[1, 4]
I =
4.Medium
xy1y = x·sin x

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

∫₀1 x·sin x dx
I =
5.Hard
xy−22

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

y = 4 − x²
A =
6.Hard
xy3y = x²eˣ

Evaluate I = ∫₀3 x²·eˣ dx.

∫₀3 x²eˣ dx
I =

Answer key

  1. 1. I = 35.33
  2. 2. V = 28.27
  3. 3. I = 2.773
  4. 4. I = 0.3012
  5. 5. A = 10.67
  6. 6. I = 98.43

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