Use Green's Theorem to Evaluate the Line Integral Along the Given

question 156

Short Answer

Use Green's Theorem to evaluate the line integral along the given positively oriented curve: $\int _ { C } \left( y ^ { 2 } - \tan ^ { - 1 } x \right) d x + ( 3 x + \sin y ) d y$ , where C is the boundary of the region enclosed by the parabola $y = x ^ { 2 }$ and the line $y = 4$ .

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Definitions:

Imports

Goods or services brought into a country from abroad for sale, which can impact a nation's balance of trade.

Trade Deficit

A situation where a country's imports of goods and services exceed its exports, resulting in a negative balance of trade.

GDP

Gross Domestic Product, the total market value of all final goods and services produced within a country in a given period of time.

Balance Of Trade

The difference between a country's exports and imports of goods and services, indicating whether a country has a trade surplus or deficit over a specific period.