Area between curves

  • #1

Homework Statement


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

symimage.gif



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]
 

Answers and Replies

  • #2
125
0
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
 
  • #3
104
0
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
 
  • #4
GAH, thanks! I should probably just stick with a calculator to solve the last parts to eliminate errors like that.
 

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