Evaluate the Line Integral $\int _ { C } \sin x d x$

question 61

Short Answer

Evaluate the line integral $\int _ { C } \sin x d x$ where $C$ is the arc of the curve $x = y ^ { 4 }$ from $( 1 , - 1 )$ to $( 1,1 )$ .

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Definitions:

Doubled Income

A situation where an individual's or entity's income increases to twice its initial amount.

Homothetic Preferences

Consumer preferences where if a bundle of goods is preferred to another, then any scaled up or down version of the bundle is also preferred based on the proportion of goods, maintaining consumption patterns.

Prices Double

A situation where the prices of goods or services increase to twice their original amount.

Quasilinear Preferences

Consumer preferences where the utility function is linear in one of the goods, indicating constant marginal utility for that good.