Use Reduction Formulas to Evaluate the Integral $$\int 8 \cos ^ { 3 } 2 x d x$$

question 453

Multiple Choice

Use reduction formulas to evaluate the integral.
- $$\int 8 \cos ^ { 3 } 2 x d x$$

• A) \(4 \sin 2 x - \frac { 4 } { 3 } \cos ^ { 3 } 2 x + C\)
• B) \(4 \sin 2 x + \frac { 4 } { 3 } \sin ^ { 3 } 2 x + C\)
• C) \(8 \sin 2 x - \frac { 8 } { 3 } \sin ^ { 3 } 2 x + C\)
• D) \(4 \sin 2 x - \frac { 4 } { 3 } \sin ^ { 3 } 2 x + C\)

---

Definitions:

Demand Curve

A graphical representation showing the relationship between the price of a good or service and the quantity demanded for a given period.

Price Elasticity

The responsiveness of the quantity demanded of a good to a change in its price.

Price Elasticity

An indicator of the degree to which the demand or supply of a product adjusts due to a variation in its cost.

Midpoint Formula

A method used in economics to calculate the elasticity of demand or supply between two points on a curve by averaging the quantities and prices.