Evaluate the Line Integral $\int _ { C } \left( y + x ^ { 2 } \right) d x + \left( 2 x + \sqrt [ 3 ] { \sin y ^ { 3 } + e ^ { y ^ { 2 } } } \right) d y$

question 46

Short Answer

Evaluate the line integral $\int _ { C } \left( y + x ^ { 2 } \right) d x + \left( 2 x + \sqrt [ 3 ] { \sin y ^ { 3 } + e ^ { y ^ { 2 } } } \right) d y$ , where C is the upper half of the circle $x ^ { 2 } + y ^ { 2 } = 1$ from $( 1,0 )$ to $( - 1,0 )$ .

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Monopolist

An entity that is the sole provider of a particular product or service in the market, having significant control over pricing.

Deadweight Loss

A loss of economic efficiency that can occur when the free market equilibrium for a good or a service is not achieved.

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The overall well-being and quality of life of the people within a society, including factors like health, happiness, and economic prosperity.

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A market condition where resources are allocated in a way that maximizes the overall benefit to society.