Posted by Francesca on .
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,
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,
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,
588 is the correct answer!**

Math 
Steve,
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