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AP® Calculus AB-BC

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Limit Definition of a Definite Integral

APCALC-XWWTNJ

State the definite integral represented by the following limit:

$$\lim_{n\rightarrow \infty }\sum_{i=1}^{n}\left ( 3+\frac{2i}{n} \right )^{3}\left ( \frac{2}{n} \right )$$

A

$\int_{3}^{5}x^{3}dx$

B

$\int_{2}^{5}x^{3}dx$

C

$\int_{3}^{5}\left ( 1+x \right )^{3}dx$

D

$\int_{2}^{5}\left ( 1+x \right )^{3}dx$