Write the limit $\lim _ { | \Delta | \rightarrow 0 } \sum _ { i = 1 } ^ { n } \left( \frac { 6 } { c _ { i } ^ { 2 } } \right) \Delta x _ { i } , \text { as a definite integral on the interval } [ 8,10 ]$ where ci is any point in the $i ^ { t h }$ subinterval.
A) $\int _ { 10 } ^ { 8 } \frac { 6 } { x ^ { 2 } } d x$
B) $\int _ { 0 } ^ { 8 } \frac { 6 } { x ^ { 2 } } d x$
C) $\int _ { 0 } ^ { 2 } \frac { 6 } { x ^ { 2 } } d x$
D) $\int _ { 0 } ^ { 10 } \frac { 6 } { x ^ { 2 } } d x$
E)$\int _ { 8 } ^ { 10 } \frac { 6 } { x ^ { 2 } } d x$

Question

Write the limit $\lim _ { | \Delta | \rightarrow 0 } \sum _ { i = 1 } ^ { n } \left( \frac { 6 } { c _ { i } ^ { 2 } } \right) \Delta x _ { i } , \text { as a definite integral on the interval } [ 8,10 ]$ where ci is any point in the $i ^ { t h }$ subinterval. 
A) $\int _ { 10 } ^ { 8 } \frac { 6 } { x ^ { 2 } } d x$
B) $\int _ { 0 } ^ { 8 } \frac { 6 } { x ^ { 2 } } d x$
C) $\int _ { 0 } ^ { 2 } \frac { 6 } { x ^ { 2 } } d x$
D) $\int _ { 0 } ^ { 10 } \frac { 6 } { x ^ { 2 } } d x$
E)$\int _ { 8 } ^ { 10 } \frac { 6 } { x ^ { 2 } } d x$

Quizplus · Accepted Answer

We see that the limit has the form of a Riemann sum, where each term is $\frac{6}{c_i^2}\Delta x_i$. So, we can rewrite the limit as the definite integral $\int_{8}^{10}\frac{6}{x^2}dx$, which corresponds to choice E.

Write the Limit Where Ci Is Any Point in The ithi ^ { t h }ith

Write the Limit Where Ci Is Any Point in The $i ^ { t h }$