Write the Limit $[ 0,8 ]$ Where $c _ { i }$

question 64

Multiple Choice

Write the limit $\lim _ { | \Delta x | \rightarrow 0 } \sum _ { i = 1 } ^ { n } 4 c _ { i } \left( 7 - c _ { i } \right) ^ { 2 } \Delta x _ { i } , \text { as a definite integral on the interval }$ $[ 0,8 ]$ where $c _ { i }$ is any point in the $i ^ { t h }$ subinterval.

• A) \( \int 4 x(7-x)^{8} d x \)
• B) \( \int_{8}^{0} 4 x^{2}(7-x)^{8} d x \)
• C) \( \int 4 c_{i}\left(7-c_{i}\right)^{2} \Delta x_{i} \)
• D)\( \int_{0}^{8} 4 x(7-x)^{2} d x \)
• E)\( \int_{0}^{c_{i}} 4 c_{i}\left(7-c_{i}\right)^{2} \Delta x_{i} \)

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