Evaluate the integral and interpret it as the area of a region

Question

7

|(3x+10) -x dx

0

Answer 1

U = 3x+10

dU = 3 dx

integral (sqrt(3x+10)) dx

= (1/3) integral ( sqrt(U)) dU

= (1/3) (2/3)U^(3/2)

= 2/9 U^(3/2)

= (2/9) (3x+10)^(3/2)

the second function integrates to (1/2)x^2

the limit as x-->0 is zero, so nothin there...

the limit as x-->7 is

(2/9) (3*7+10)^(3/2) =

(2/9) (31)^(3/2) - 49/2 =

13.855710055051262130156357836994