Help finding area of the region between x-axis and the graph.

• Oct 3rd 2010, 02:47 PM
solidstatemath
Help finding area of the region between x-axis and the graph.
Q: Find the total area of the region between the x-axis and the graph of y= -x^2 -3x, -8 smaller or equal to x and x smaller or equal to 2.

Right now I'm doing cal2 and we have been using integrals to solve most problems. How can I solve this one?

Now I think the integrals should be -8, -3 and -3, 0 and 0, 2.
• Oct 3rd 2010, 03:18 PM
skeeter
Quote:

Originally Posted by solidstatemath
Q: Find the total area of the region between the x-axis and the graph of y= -x^2 -3x, -8 smaller or equal to x and x smaller or equal to 2.

Right now I'm doing cal2 and we have been using integrals to solve most problems. How can I solve this one?

Now I think the integrals should be -8, -3 and -3, 0 and 0, 2.

let $f(x) = -x^3-3x$

$\displaystyle A = -\int_{-8}^{-3} f(x) \, dx + \int_{-3}^{0} f(x) \, dx - \int_0^2 f(x) \, dx$
• Oct 3rd 2010, 03:46 PM
solidstatemath
Right! They must follow, how could I ignore that! Thanks man I'll post once I've solved it.
• Oct 3rd 2010, 03:59 PM
solidstatemath
I end up with -223/3 for the area. Since it must be the absolute value it is 223/3. What did you get?
• Oct 3rd 2010, 04:10 PM
skeeter
Quote:

Originally Posted by solidstatemath
I end up with -223/3 for the area. Since it must be the absolute value it is 223/3. What did you get?

My calculator says the area = 277/3 ... don't you have a calculator to check your work?
• Oct 3rd 2010, 04:48 PM
solidstatemath
Yes I recalculated and got it. Must had a bad sign somewhere.