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

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

y = 2x0 ≤ x ≤ 2

V =

2.Easy

Evaluate I = ∫₋₁² (−2x³ + 6x + 6) dx.

f(x) = −2x³ + 6x + 6[−1, 2]

I =

3.Medium

Evaluate I = ∫₀² e^−x dx.

f(x) = e^−x[0, 2]

I =

4.Medium

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

Evaluate I = ∫₀^2.5 x²·eˣ dx.

∫₀^2.5 x²eˣ dx

I =

6.Hard

Find the area A of the region between the parabola y = 1 − x² and the x-axis.

y = 1 − x²

A =

Answer key

1. V = 33.51
2. I = 19.5
3. I = 0.8647
4. V = 25.13
5. I = 37.59
6. A = 1.333

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