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 - 2x1/2
Then I integrated it
2. 0∫2(x - 2x1/2)dx
Then I used the antiderivative
3. (x2/2) - (4/3)x3/2
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:
(4/2) - (4/3)√23
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?