Finding the area between f(x) = 6x - x² and g(x) = x²

[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.