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
xy2.5y = xe2x​

Evaluate I = ∫₀2.5 x·e2x dx.

∫₀2.5 x·e2x dx
I =
2.Easy
xy1y = xex/2​

Evaluate I = ∫₀1 x·ex/2 dx.

∫₀1 x·ex/2 dx
I =
3.Medium
xy28

Evaluate I = ∫28 4/x dx.

f(x) = 4/x[2, 8]
I =
4.Medium
xy2y = √(4x)

The region under y = √(4x) from x = 0 to x = 2 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(4x)0 ≤ x ≤ 2
V =
5.Hard
xyy = x2​y = 2x

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

y = x2y = 2x
A =
6.Hard
xy−22

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

y = 4 − x²
A =

Answer key

  1. 1. I = 148.7
  2. 2. I = 0.7026
  3. 3. I = 5.545
  4. 4. V = 25.13
  5. 5. A = 1.333
  6. 6. A = 10.67

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