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tangibleLime

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## Homework Statement

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.

## Homework Equations

[tex]\int_a^b [f(x) - g(x)]dx[/tex]

## The Attempt at a Solution

[tex]f(x) = 6x-x^2[/tex]

[tex]g(x) = x^2[/tex]

[tex]a = 0, b = 3[/tex]

[tex]\int_a^b [f(x) - g(x)]dx[/tex]

[tex]\int_0^3 [(6x-x^2)-(x^2)]dx[/tex]

[tex]((3x^2-\frac{x^3}{3})-(\frac{x^3}{3})\vert_0^3[/tex]

[tex]((3(3)^2-\frac{(3)^3}{3})-(\frac{(3)^3}{3}))[/tex]

[tex]((24)-(3))[/tex]

[tex]21[/tex]