   Chapter 4.3, Problem 69E

Chapter
Section
Textbook Problem

Finding a Riemann Sum Find the Riemann sum for f ( x ) = x 2 + 3 x over the interval [0, 8], where x 0 = 0 , x 1 = 1 , x 2 = 3 , x 3 = 7 ,   and   x 4 = 8 and where c 1 = 1 , c 2 = 2 , c 3 = 5 ,   and   c 4 = 8 To determine

To calculate: The Riemann sum for f(x)=x2+3x over the interval [0,8].

Explanation

Given:

Function as, f(x)=x2+3x

x0=0,x1=1,x2=3,x3=7, and x4=8

c1=1,c2=2,c3=5, and c4=8

The diagram of the function is given below.

Formula used:

If ci is any point in the ith subinterval, then the sum

i=1nf(ci)Δxi, xi1cixi

is called a Riemann sum of f for the partition Δ.

Calculation:

Function is given as f(x)=x2+3x over the interval [0,8].

Therefore, a=0 and b=8. Also, n=4

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