Express the limit as a deﬁnite integral.
- $\text { where } P \text { is a partition of }[-2,3]$
A) $\int _ { - 2 } ^ { 3 } 7 x ^ { 6 } d x$
B) $\int _ { 3 } ^ { - 2 } x ^ { 7 } d x$
C) $\int _ { - 2 } ^ { 3 } x ^ { 7 } d x$
D) $\int _ { 1 } ^ { \mathrm { n } } \mathrm { xdx }$

Question

Express the limit as a deﬁnite integral.
- $\text { where } P \text { is a partition of }[-2,3]$ 
A) $\int _ { - 2 } ^ { 3 } 7 x ^ { 6 } d x$ 
B) $\int _ { 3 } ^ { - 2 } x ^ { 7 } d x$ 
C) $\int _ { - 2 } ^ { 3 } x ^ { 7 } d x$ 
D) $\int _ { 1 } ^ { \mathrm { n } } \mathrm { xdx }$

Quizplus · Accepted Answer

Since the limit is asking for the area under a curve on the interval $[-2,3]$, we can express it as a definite integral. Looking at the options, only option C has the same variable and power as the limit expression, so we can set it equal to the integral: $$\lim_{||P|| 	o 0} \sum_{i=1}^{n} 7 \left(\frac{3-(-2)}{n}ight)^7 x_i^6 = \int_{-2}^3 7x^6 dx$$

Express the Limit as a Deﬁnite Integral where P is a partition of [−2,3]\text { where } P \text { is a partition of }[-2,3] where P is a partition of [−2,3]

Express the Limit as a Deﬁnite Integral $\text { where } P \text { is a partition of }[-2,3]$