Posted by **Francesca ** on Thursday, June 14, 2012 at 12:10pm.

Use the definite integral to find the area between the x-axis over the indicated interval.

f(x) = 36 - x^2; [-1,13]

So, what does be the area between the x-axis and f(x) equal? Thank you for any help! I'm really confused with this problem!

- Math -
**Steve**, Thursday, June 14, 2012 at 12:58pm
Do you mean algebraic (signed) area? If so, that is -686/3.

If you mean actual physical area, where area below the axis is also considered positive, then you have to break the area into the part above the axis [-1:6] and below the axis [6:13]. Doing it that way, we get 588.

- Math -
**Francesca **, Thursday, June 14, 2012 at 1:14pm
588 is the correct answer? But, I don't understand how to get to that number. How did you calculate that? Sorry, that may be a lot to type out

- Math -
**Francesca **, Thursday, June 14, 2012 at 1:14pm
588 is the correct answer!**

- Math -
**Steve**, Thursday, June 14, 2012 at 5:39pm
The graph crosses the x-axis at (6,0)

integrate 36-x^2 from -1:6 to get the positive area

integrate -(36-x^2) from 6:13 to add the area below the axis instead of subtracting it

∫[-1,6](36-x^2) + ∫[6,13](x^2-36)

= (36x - x^3/3)[-1:6] + (x^3/3 - 36x)[6,13]

539/3 + 1225/3 = 1764/3 = 588

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