Evaluate line integral(x+sqrt(y)) over y=x^2 from (0,0) to (1,1) and y=x from (1,1) to (0,0)
The Attempt at a Solution
I set up integral from 0 to 1 of 2t(sqrt(1+4t^2))dt for the parabola part and then added integral from 0 to 1 of (t+sqrt(t))(sqrt2)dt and I am getting 5^(3/2)/6-1/6+7(sqrt2)/6.
The textbook gives the answer to be similar to mine except it is minus 7(sqrt2)/6.
I added the two integrals, but I would receive the same answer as the book if I subtracted the second integral from the first instead of adding the two (or rather, did integral from 1 to 0 for the second one). However, I was under the impression you are supposed to use the lower bounds to higher bounds for line integrals.
Thanks for the help with this one, thanks.