Lower level algebra Question Concerning the Solution to a Calculus Problem

[Asphyxiated]

Nevermind I totally got it now, sorry to waste anyones time!

 

[Mark44]

Homework Statement

$$\int^{2}_{0} (x+1)^{1/2} dx$$

The Attempt at a Solution

This problem is very easy to solve, I have no problem with that, but I will list my solution anyway. The problem I am having is finding the solution to the problem that is in the book. Our solutions are the same when approximated to decimals but I have no idea how they got the exact form of the solution, so I am hoping someone can help me here, the problem is solved like so:

$$\frac {2}{3}(x+1)^{3/2} +C$$

well that's the indefinite integral anyway, so the solution looks something like this for the definite integral:

$$\frac {2}{3}(2)^{3/2} - \frac {2}{3}(0)^{3/2}$$

Your mistake is in the line above. The expression raised to the 3/2 power in your antiderivative is x + 1, not x so both your terms above are incorrect. After evaluating the antiderivative at the two endpoints you should have (2/3)[(2 + 1)^(3/2) - 1^(3/2)].

and the last portion is going to be zero, so the solution is just:

$$\frac {2}{3}(2)^{3/2}$$

right? For exact form anyway? Which could be written this way:

$$\frac {2}{3} \sqrt{2^{3}}$$

but what they want is:

$$\frac {2}{3} (3\sqrt{3}-1)$$

I know they are the same answers so I just want to know how to get to that answer from the answer I have.

Thanks greatly! And I am sorry if this is really obvious but I can't for the life of me remember this.

 

[Asphyxiated]

yeah I seen that, I just did a lot of correcting to that post, so please take a look at it again because it has changed