Calculus AB
posted by janki on .
y=6x y=x^2
Find the area of the region by
integrating with respect to x.
Find the area of the region by integrating with respect to y.

i got the intersection pts to be(3,9)and (2,4)....i then took the integral and found the answer to be 20.8333 for both parts...HOWEVER...its wrong! please help!

Your intersection points are correct
Method1:
the effective height of a slice = 6x  x^2
area = ∫ (6x  x^2) dx from x = 3 to 2
= [6x  x^2/2  x^3/3] from 3 to 2
= 12  2  8/3  (18 9/2  (27/3) )
= 10  8/3 + 9 + 9/2
= 19 + 11/6
= 20 5/6 or 125/6 , so you were right