Sketch Region Enclosed by f(x) & g(x): Integrate w/ Respect to X or Y

[tangibleLime]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

f(x) = 6x-x^2
g(x) = x^2

a = 0, b = 3

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

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

((3x^2-\frac{x^3}{3})-(\frac{x^3}{3})\vert_0^3

((3(3)^2-\frac{(3)^3}{3})-(\frac{(3)^3}{3}))

((24)-(3))

21

 

[mynameisfunk]

nope. you messed up. check your algebra. to make it easier, turn the 2nd line into 6x-2x^2. I am typically always wrong whenever i post on this forum, BUT I got 9

 

[number0]

Yes, you did mess up on the algebra at the last part.

3 * 3^3 = 27 not 24.

And 3^3/3 = 9, not 3! You have 2 of them so 9 * 2 = 18.

27 - 18 = 9

 

[tangibleLime]

GAH, thanks! I should probably just stick with a calculator to solve the last parts to eliminate errors like that.