Question

If f(x) = 5x2 − 2x, 0 ≤ x ≤ 3, evaluate the Riemann sum with n = 6, taking the sample points to be right endpoints. R6 =

Answer 1

Answer:

46.375

Step-by-step explanation:

Given information:

$f(x)=5x^2-2x$

where, 0 ≤ x ≤ 3.

We need to divde the interval [0,3] in 6 equal parts.

The length of each sub interval is

$\dfrac{b-a}{n}=\dfrac{3-0}{6}=0.5$

Right end points are 0.5, 1, 1.5, 2, 2.5, 3.

The value function on each right end point are

$f(0.5)=5(0.5)^2-2(0.5)=0.25$

$f(1)=5(1)^2-2(1)=3$

$f(1.5)=5(1.5)^2-2(1.5)=8.25$

$f(2)=5(2)^2-2(2)=16$

$f(2.5)=5(2.5)^2-2(2.5)=26.25$

$f(3)=5(3)^2-2(3)=39$

Riemann sum:

$\sum_{n=1}^6 f(x_n)\Delta x_n$

$Sum=[f(0.5)+f(1)+f(1.5)+f(2)+f(2.5)+f(3)]\times 0.5$

$Sum=[0.25+3+8.25+16+26.25+39]\times 0.5$

$Sum=92.75\times 0.5$

$Sum=46.375$

Therefore, the Riemann sum with n = 6 is 46.375.