Evaluate the Integral $$\int _ { 0 } ^ { 1 / 2 } 3 \sin ^ { 4 } 2 \pi x d x$$

question 214

Multiple Choice

Evaluate the integral.
- $$\int _ { 0 } ^ { 1 / 2 } 3 \sin ^ { 4 } 2 \pi x d x$$

• A) \(\frac { 9 } { 16 }\)
• B) \(\frac { 9 } { 8 } - \frac { 3 } { 8 \pi }\)
• C) \(\frac { 9 } { 16 } - \frac { 3 } { \pi }\)
• D) \(\frac { 9 } { 8 }\)

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Definitions:

Balance Surplus

An economic situation where the income or supply exceeds the expenditure or demand, leading to a surplus.

Balance Deficit

The economic condition where total expenditures exceed total revenues in a given period, often in reference to national budgets or trade balances.

Current Account Deficit

Occurs when a country's total imports of goods, services, and transfers are greater than its total exports, indicating that it is spending more on foreign trade than it is earning.

Capital Account Deficit

Occurs when a country's total payments from its capital account transactions exceed its total receipts.