A function is to be integrated on the interval using a Riemann sum with equal…

MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

A function

g

is to be integrated on the interval

[-2,3]

using a Riemann sum with equal subintervals and right endpoints. (a) If each subinterval is to have width

\Delta x=0.25

, determine the exact number of subintervals

n

required. Show all supporting computations. (b) For the value of

n

found in part (a), write an explicit formula for the

i

-th right-endpoint sample point

x_{i}

in terms of

i

. Your formula should be valid for all integers

i

with

1\le i\le n

. (c) Using your

x_{i}

from part (b), express the corresponding Riemann sum (before letting

n\to\infty

) that approximates

\displaystyle\int_{-2}^{3} g(x)\,dx