Get the area between two curvess

[madinsane]

Okay, so here are the two functions, f(x)= sqrt(x+3) and g(x) = (x+3)/2
my first step was to get the intersection points and it came out to be x=1 or -3
Then I drew a graph and that told me that the function sqrt(x+3) is always above the other function on the entire interval. So then I did integral f(x)-g(x) dx with upper and lower limits 1 and -3 and the integral gave me (using u substitution as well) 2/3(x+3)^3/2 - 1/4 x^2 +3/2x and then I put in the x values and got 13.3.

Okay so the problem is that the answer in the book is 4/3 and I have no idea where I have gone wrong. Can anyone put me on the right track and tell me where I went wrong

 

[MarneMath]

I believe the problem is in the integral. That x term looks wrong, I suggest you integrate again and see where you went wrong, because yours is different than my solution and my solution gets the right answer.

Just to be a bit more clear, your actual integral is correct, but you made an error integrating.

edit:

Misread something, but yeah what arildno says works :).

 

[arildno]

Your flaw lies in your lack of parentheses in your integrated -g, you should have -(1/4x^2+3/2x) as your choice of anti-derivative, rather than what you wrote.

 

[madinsane]

Thank you. I realize my error now :)