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 = √(4x) from x = 0 to x = 4 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(4x)0 ≤ x ≤ 4

V =

2.Easy

Evaluate I = ∫₁² (−3x³ + 6x − 4) dx.

f(x) = −3x³ + 6x − 4[1, 2]

I =

3.Medium

Evaluate I = ∫₁⁴ x·ln x dx.

∫₁⁴ x ln x dx

I =

4.Medium

Evaluate I = ∫₀² e^x dx.

f(x) = e^x[0, 2]

I =

5.Hard

Evaluate I = ∫₀^0.5 x²·eˣ dx.

∫₀^0.5 x²eˣ dx

I =

6.Hard

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

y = 2xy = x²

V =

Answer key

1. V = 100.5
2. I = −6.25
3. I = 7.34
4. I = 6.389
5. I = 0.0609
6. V = 13.4

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