Hi, so I got this problem:

f(x) = x - 2√x, intervals are: [0,2]

This is what I did:

First I turned the square root sign into an exponent

1. x - 2x^{1/2}

Then I integrated it

2._{0}∫^{2}(x - 2x^{1/2})dx

Then I used the antiderivative

3. (x^{2}/2) - (4/3)x^{3/2}

Just letting you know in case if you were wondering about the (4/3), since I know that it would be multiplied by (2/3) since it's the inverse of the exponent, then it was multiplied by the 2 on the outside.

Then I did f(b) - f(a), which means plugging in 2, then plugging in 0, and subtracting it from each other, though I left out the 0 part because it makes everything 0, so I only plugged in the 2, therefore I did not need to subtract

4.This is what I got:

(2)^{2}/2 -(4/3)(2)^{3/2}

(4/2) - (4/3)√2^{3}

2 - (4/3)√(4*2)

2 - (4/3) * (2√2)

2 - (8√2)/3

I don't really know where to go on from there.

Someone showed me this (and by the way, it's the correct answer in the back of the book as well)

But I am really confused on how they did those next steps!

I see the left side, which is f(c)(2-0), and I'm confused what that means, and where the 6 came from on the right side.

And so on.

Can someone explain to me or help me find a simplier way for me to understand?

Thanks!