Question

$\int_c -ydx + xdy$

$C=y^2 =3x$ from (3,3) to(0,0)

• A. 9
• B. 3
• C. 6
• D. 2

Answer 1

Answer:

B. 3

$y^2 = 3x \to x = \frac{y^2}{3}$

$dx=\frac{2y}{3}dy$

$\int_{y=3}^0-y \frac{2}{3}ydy + \frac{y^2}{3}dy = \int_{y=3}^0\frac{-2}{3}y^2dy+\frac{y^2}{3}dy$

$=\int_0^3\frac{-1}{3}y^2dy$

$=\frac{1}{3}\int_0^3y^2dy$

$=\frac{1}{3}[\frac{y^3}{3}]_0^3$

$=3$