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−12

Evaluate I = ∫−12 (−2x2 − 6x − 2) dx.

f(x) = −2x2 − 6x − 2[−1, 2]
I =
2.Easy
xy2.5y = xe2x​

Evaluate I = ∫₀2.5 x·e2x dx.

∫₀2.5 x·e2x dx
I =
3.Medium
xy26

Evaluate I = ∫26 4/x dx.

f(x) = 4/x[2, 6]
I =
4.Medium
xy4y = √(4x)

The region under y = √(4x) from x = 0 to x = 4 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(4x)0 ≤ x ≤ 4
V =
5.Hard
xyy = 0.5x2​y = 4x

Find the area A of the region enclosed by y = 0.5x2 and y = 4x.

y = 0.5x2y = 4x
A =
6.Hard
xy1.5y = x²eˣ

Evaluate I = ∫₀1.5 x²·eˣ dx.

∫₀1.5 x²eˣ dx
I =

Answer key

  1. 1. I = −21
  2. 2. I = 148.7
  3. 3. I = 4.394
  4. 4. V = 100.5
  5. 5. A = 42.67
  6. 6. I = 3.602

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