Evaluate the Integral $\int _ { 0 } ^ { 1 } x ^ { 2 } ( x + 2 ) ^ { 2 } \mathrm {~d} x$

question 81

Multiple Choice

Evaluate the integral. $\int _ { 0 } ^ { 1 } x ^ { 2 } ( x + 2 ) ^ { 2 } \mathrm {~d} x$

• A) \(- \frac { 253 } { 60 }\)
• B) \(\frac { 38 } { 15 }\)
• C) \(\frac { 38 } { 5 }\)
• D) \(\frac { 38 } { 3 }\)
• E) \(\frac { 481 } { 30 }\)

---

Definitions:

Budget Line

A graphical representation of all possible combinations of two goods which can be purchased with a given budget at fixed prices.

Utility Function

A utility function is a mathematical representation in economics that depicts an individual's preference ranking over a set of goods or outcomes, showing the level of satisfaction or utility derived from them.

Nuts

Hard-shelled edible seeds of certain plants, often rich in oil and nutrients.

Berries

Small, juicy fruits with a high vitamin content, often edible and ranging in flavor from sweet to tart, used in various culinary applications.