Find the Value of the Integral $\int _ { 0 } ^ { x / 2 } \cos ^ { 3 } x d x$

question 176

Multiple Choice

Find the value of the integral $\int _ { 0 } ^ { x / 2 } \cos ^ { 3 } x d x$

• A)1
• B) \(\frac { 1 } { 3 }\)
• C) \(\frac { 2 } { 3 }\)
• D)2
• E)3
• F) \(\frac { \pi } { 2 }\)
• G) \(\frac { 1 } { 6 }\)
• H) \(\frac { \pi } { 2 } - \frac { \pi ^ { 3 } } { 24 }\)

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Definitions:

Spending Multiplier

A concept in economics that quantifies the impact of a change in fiscal policy on the overall economy, indicating how an initial change in spending leads to a larger change in income and output.

Potential Output

The maximum amount of goods and services an economy can produce when it uses its resources fully and efficiently, without causing inflation.

Net Taxes

The total taxes paid to the government minus transfer payments and subsidies received from the government.

Aggregate Demand

The total quantity of goods and services demanded across all levels of an economy at a given price level and in a given time period.