Posted by math on .
Find the area of the shaded region.
View the graph and image at:
postimg.o rg/image/dg4kt89v1/
Please help me explain this one. I know the ans to this one but can not work out.

math 
Reiny,
you have to do in in two parts
we need the xintercept:
0 = √x3
√x = 3
x = 9
area from 0 to 9 + area from 9 to 16
(If you do it in one calculation from 0 to 16, the area which is below the xaxis will work its way into the answer as a negative area)
y = √x  3
Area = ∫(x^(1/2) + 3) dx from 0 to 9 + ∫(x^(1/2)  3) dx from 9 to 16
= ((2/3)x^(3/2) + 3x)from 0 to 9 + ((2/3)x^(3/2)  3x) from 9 to 16
=(2/3)(27) + 27  0 + (2/3)(64)  48  ((2/3)(27)  27)
= 18 + 27 + 128/3  48  18 + 27
= 38/3