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
xy12

Evaluate I = ∫12 (−3x3 + x − 2) dx.

f(x) = −3x3 + x − 2[1, 2]
I =
2.Easy
xy14

Evaluate I = ∫14 (2x3 + 4x − 4) dx.

f(x) = 2x3 + 4x − 4[1, 4]
I =
3.Medium
xy12y = x ln x

Evaluate I = ∫₁2 x·ln x dx.

∫₁2 x ln x dx
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
xy1y = x²eˣ

Evaluate I = ∫₀1 x²·eˣ dx.

∫₀1 x²eˣ dx
I =
6.Hard
xyy = 2x2​y = x

Find the area A of the region enclosed by y = 2x2 and y = x.

y = 2x2y = x
A =

Answer key

  1. 1. I = −11.75
  2. 2. I = 145.5
  3. 3. I = 0.6363
  4. 4. V = 6.283
  5. 5. I = 0.7183
  6. 6. A = 0.04167

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