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 dx.

∫₀^0.5 x·e^−x dx

I =

2.Easy

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 =

3.Medium

Evaluate I = ∫₂⁴ 1/x dx.

f(x) = 1/x[2, 4]

I =

4.Medium

Evaluate I = ∫₁² 4/x dx.

f(x) = 4/x[1, 2]

I =

5.Hard

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

y = 9 − x²

A =

6.Hard

The region between the line y = 3x and the parabola y = x² is rotated about the x-axis. Find the volume V of the solid.

y = 3xy = x²

V =

Answer key

1. I = 0.0902
2. V = 25.13
3. I = 0.6931
4. I = 2.773
5. A = 36
6. V = 101.8

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