Provide an Appropriate Response $\lim _ { n \rightarrow \infty } \sum _ { i = 1 } ^ { n } \left( \frac { 4 i } { n } \right) ^ { 2 } \frac { 4 } { n }$

question 143

Multiple Choice

Provide an appropriate response.
-What definite integral is represented by $\lim _ { n \rightarrow \infty } \sum _ { i = 1 } ^ { n } \left( \frac { 4 i } { n } \right) ^ { 2 } \frac { 4 } { n }$ ? Use the Fundamental Theorem to evaluate the integral.

• A) \(\int _ { 0 } ^ { 1 } 4 x ^ { 2 } \mathrm { dx } = \frac { 4 } { 3 }\)
• B) \(\int _ { 0 } ^ { 4 } x ^ { 2 } d x = \frac { 64 } { 3 }\)
• C) \(\int _ { 1 } ^ { 4 } x ^ { 2 } d x = 21\)
• D) \(\int _ { 0 } ^ { 4 } x ^ { 3 } d x = 64\)