Posted by Francesca on Thursday, June 14, 2012 at 12:10pm.
Use the definite integral to find the area between the xaxis over the indicated interval.
f(x) = 36  x^2; [1,13]
So, what does be the area between the xaxis 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 xaxis at (6,0)
integrate 36x^2 from 1:6 to get the positive area
integrate (36x^2) from 6:13 to add the area below the axis instead of subtracting it
∫[1,6](36x^2) + ∫[6,13](x^236)
= (36x  x^3/3)[1:6] + (x^3/3  36x)[6,13]
539/3 + 1225/3 = 1764/3 = 588
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