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 (−x3 − x − 5) dx.

f(x) = −x3 − x − 5[−2, −1]
I =
2.Easy
xy2y = xex​

Evaluate I = ∫₀2 x·ex dx.

∫₀2 x·ex dx
I =
3.Medium
xy12

Evaluate I = ∫12 2/x dx.

f(x) = 2/x[1, 2]
I =
4.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 =
5.Hard
xyy = 0.5x2​y = 3x

Find the area A of the region enclosed by y = 0.5x2 and y = 3x.

y = 0.5x2y = 3x
A =
6.Hard
xy2y = x²eˣ

Evaluate I = ∫₀2 x²·eˣ dx.

∫₀2 x²eˣ dx
I =

Answer key

  1. 1. I = 0.25
  2. 2. I = 8.389
  3. 3. I = 1.386
  4. 4. V = 6.283
  5. 5. A = 18
  6. 6. I = 12.78

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