Evaluate the Line Integral $\int _ { C } x y ^ { 2 } d x + x ^ { 2 } y d y$

Short Answer

Evaluate the line integral $\int _ { C } x y ^ { 2 } d x + x ^ { 2 } y d y$ :
(a) if $C$ is the curve $x = \cos t , y = \sin t , \quad 0 \leq t \leq \pi$ , the top half of the unit circle from $( 1,0 )$ to $( - 1,0 )$ .(b) if $C$ is the line segment from $( 1,0 )$ to $( - 1,0 )$ .