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

question 28

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 $( - 1,0 )$ .

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Efficiency Measurement

The process of evaluating the performance of a system or process in terms of resource utilization.

Volume

In business, it refers to the quantity of an item produced or traded, often used to measure the level of activity in a business or market.

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The total count or population of individuals within a specified area or group.

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