Evaluate the Integral by Using a Substitution Prior to Integration $$\int x \sqrt { 2 - x } d x$$

question 73

Multiple Choice

Evaluate the integral by using a substitution prior to integration by parts.
- $$\int x \sqrt { 2 - x } d x$$

• A) \(\frac { 2 } { 3 } x ( 2 - x ) ^ { 3 / 2 } + \frac { 4 } { 15 } ( 2 - x ) ^ { 5 / 2 } + C\)
• B) \(- \frac { 2 } { 3 } x ( 2 - x ) ^ { 3 / 2 } + \frac { 4 } { 15 } ( 2 - x ) ^ { 5 / 2 } + C\)
• C) \(- \frac { 2 } { 3 } x ( 2 - x ) ^ { 3 / 2 } - \frac { 4 } { 15 } ( 2 - x ) ^ { 5 / 2 } + C\)
• D) \(- \frac { 2 } { 3 } x ( 2 - x ) ^ { 3 / 2 } - \frac { 2 } { 5 } ( 2 - x ) ^ { 5 / 2 } + C\)

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Definitions:

Digestion

The process by which food is broken down into smaller components that can be absorbed and utilized by the body.

Emulsification

The process by which large fat droplets are broken down into smaller, uniformly distributed particles, usually aided by substances called emulsifiers.

Lipid Digestion

The process of breaking down fats into fatty acids and glycerol, mainly occurring in the small intestine.

Surface Area

The total area of the surface of a three-dimensional object.