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

y = x0 ≤ x ≤ 2

V =

2.Easy

Evaluate I = ∫₀³ x·e^2x dx.

∫₀³ x·e^2x dx

I =

3.Medium

The region under y = 0.5x from x = 0 to x = 2 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 2

V =

4.Medium

Evaluate I = ∫₁⁵ 2/x dx.

f(x) = 2/x[1, 5]

I =

5.Hard

Evaluate I = ∫₀^1.5 x²·eˣ dx.

∫₀^1.5 x²eˣ dx

I =

6.Hard

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

y = 4 − x²

A =

Answer key

1. V = 8.378
2. I = 504.5
3. V = 2.094
4. I = 3.219
5. I = 3.602
6. A = 10.67

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