Graph the Integrand and Use Areas to Evaluate the Integral $$\int _ { - 6 } ^ { 6 } \sqrt { 36 - x ^ { 2 } } d x$$

question 46

Multiple Choice

Graph the integrand and use areas to evaluate the integral.
- $$\int _ { - 6 } ^ { 6 } \sqrt { 36 - x ^ { 2 } } d x$$

• A) \(6 \pi\)
• B) 36
• C) \(36 \pi\)
• D) \(18 \pi\)

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Definitions:

Marginal Utility

An increase in utility or pleasure from consuming one more unit of a particular good or service.

Essential Water

The minimum amount of water required for basic human needs and sustainable living.

Nonessential Diamonds

Diamonds categorized as luxury items, not required for basic living or survival needs.

Diamond-water Paradox

The contradiction observed in value theory where essential goods like water have low prices, while non-essential goods like diamonds have high prices.