suppose I want to evaluate the line integral:
$\int_{c}(x+2y)dx+x^2dy$
Where $c$ consists of the line segments from $(0,0)$ to $(2,1)$, and from $(2,1)$ to $(3,0)$
My parametrization are as follows:
$C_i: x=2t, y=t$ where $t\in[0,1]$
$C_{ii}: x=2+t, y=1-t$ where $t\in[0,1]$
I then get:
$\int_{0}^{1}(2t+2t)2 + (2t)^2 dt$ + $\int_{0}^{1}(2+t)+2(1-t)-(2+t)^2 dt$
Integrating this gives me a value of $\frac{7}{2}$, but the answer in the textbook is $\frac{5}{2}$
I'm not sure what I did wrong here, if anyone can lead me in the right direction I'd greatly appreciate it.
Thanks.
I think $$\int _0^1\left((2t+2t)2+(2t)^2+(2+t)+2(1-t)-(2+t)^2\right)dt=\frac{5}{2}$$ so I think you are correct but the last step is not $\frac{7}{2}$ hope it can help.