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

Evaluate I = ∫₀^0.5 x·e^x/2 dx.

∫₀^0.5 x·e^x/2 dx

I =

2.Easy

Evaluate I = ∫₀² (3x³ + 5x + 4) dx.

f(x) = 3x³ + 5x + 4[0, 2]

I =

3.Medium

The region under y = 0.5x from x = 0 to x = 3 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 3

V =

4.Medium

Evaluate I = ∫₀² e^0.5x dx.

f(x) = e^0.5x[0, 2]

I =

5.Hard

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

y = x²y = 2x

A =

6.Hard

Evaluate I = ∫₀² x²·eˣ dx.

∫₀² x²eˣ dx

I =

Answer key

1. I = 0.1479
2. I = 30
3. V = 7.069
4. I = 3.437
5. A = 1.333
6. I = 12.78

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