Answer
$\int_C(\sqrt {1+x^{3}}dx+2xydy=3$
Work Step by Step
Green's Theorem: $\int_C Pdx+Qdy=\int\int_D(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y})dA$
$\int_C(\sqrt {1+x^{3}}dx+2xydy=\int\int_D2ydy=\int_{0}^{1}\int_{0}^{3x}2ydydx$
$=\int_{0}^{1}9x^2dx$
$=3$
Hence, $\int_C(\sqrt {1+x^{3}}dx+2xydy=3$
