Find the Area of the Surface Obtained by Rotating the Curve

question 101

Short Answer

Find the area of the surface obtained by rotating the curve about the $y$ -axis.
$$x = y ^ { 3 } , 0 \leq y \leq 1$$

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Definitions:

Marginal Cost

The expense increase associated with creating an additional unit of a product or service.

Mix of Output

The combination or range of different goods or services produced by an economy or firm, reflecting its production choices and strategy.

Market Failure

A circumstance where the distribution of goods and services through an unregulated market fails to be efficient, frequently resulting in a decrease in overall social welfare.

Externalities

Expenses or advantages impacting individuals who did not decide to bear those expenses or advantages.