# How do you evaluate this line integral, where C is the given curve?

Evaluate the line integral $$\int_C (x+2y)dx + x^2dy,$$ where $C$ consists of line segments from $(0,0)$ to $(2,1)$ and from $(2,1)$ to $(3,0)$.

How do you solve this? I split them up but got a negative answer.

For $C_1$ got, $\langle t, 1/2t\rangle$, $0 \leq t \leq 2$.

For $C_2$ got, $\langle t, t-3\rangle$, $2 \leq t \leq 3$.

• $C_2$ is incorrect. Check the point at $t = 2$. – Michael Albanese Apr 29 '13 at 6:51
• How about $(t,3-t)$? – oldrinb Apr 29 '13 at 6:53
• $C_1 : y = t/2$ – Halil Duru Apr 29 '13 at 8:01

$I_x=\int_0^2 (3t/2)dt+\int_2^3 (6-t) dt=13/2$
$I_y=\int _0^1 4t^2 dt++\int_1^0 (3-t)^2dt=-5$
$I=I_x+I_y=3/2$