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−10

Evaluate I = ∫−10 (−4x2 − 5x + 7) dx.

f(x) = −4x2 − 5x + 7[−1, 0]
I =
2.Easy
xy12

Evaluate I = ∫12 (−x2 − 2x − 3) dx.

f(x) = −x2 − 2x − 3[1, 2]
I =
3.Medium
xy4y = √(x)

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

y = √(x)0 ≤ x ≤ 4
V =
4.Medium
xy03

Evaluate I = ∫03 e2x dx.

f(x) = e2x[0, 3]
I =
5.Hard
xy−33

Find the area A of the region between the parabola y = 9 − x² and the x-axis.

y = 9 − x²
A =
6.Hard
xy1y = x²eˣ

Evaluate I = ∫₀1 x²·eˣ dx.

∫₀1 x²eˣ dx
I =

Answer key

  1. 1. I = 8.167
  2. 2. I = −8.333
  3. 3. V = 25.13
  4. 4. I = 201.2
  5. 5. A = 36
  6. 6. I = 0.7183

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