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^2x dx.

∫₀^0.5 x·e^2x dx

I =

2.Easy

The region under y = 2x from x = 0 to x = 3 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 2x0 ≤ x ≤ 3

V =

3.Medium

Evaluate I = ∫₀¹ e^0.5x dx.

f(x) = e^0.5x[0, 1]

I =

4.Medium

Evaluate I = ∫₀¹ e^−0.5x dx.

f(x) = e^−0.5x[0, 1]

I =

5.Hard

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

y = x²y = x

A =

6.Hard

Evaluate I = ∫₀^1.5 x²·eˣ dx.

∫₀^1.5 x²eˣ dx

I =

Answer key

1. I = 0.25
2. V = 113.1
3. I = 1.297
4. I = 0.7869
5. A = 0.1667
6. I = 3.602

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