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 = ∫₀² x·e^x/2 dx.

∫₀² x·e^x/2 dx

I =

2.Easy

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 =

3.Medium

Evaluate I = ∫₀¹ 2x·(x² + 1)² dx.

f(x) = 2x·(x² + 1)²[0, 1]

I =

4.Medium

Evaluate I = ∫₀^π x·cos x dx (x in radians).

∫₀^π x·cos x dx

I =

5.Hard

Evaluate I = ∫₀^1.5 x²·eˣ dx.

∫₀^1.5 x²eˣ dx

I =

6.Hard

The region between the line y = 2x and the parabola y = 0.5x² is rotated about the x-axis. Find the volume V of the solid.

y = 2xy = 0.5x²

V =

Answer key

1. I = 4
2. V = 7.069
3. I = 2.333
4. I = −2
5. I = 3.602
6. V = 107.2

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