Answer:
46.375
Step-by-step explanation:
Given information:
[tex]f(x)=5x^2-2x[/tex]
where, 0 ≤ x ≤ 3.
We need to divde the interval [0,3] in 6 equal parts.
The length of each sub interval is
[tex]\dfrac{b-a}{n}=\dfrac{3-0}{6}=0.5[/tex]
Right end points are 0.5, 1, 1.5, 2, 2.5, 3.
The value function on each right end point are
[tex]f(0.5)=5(0.5)^2-2(0.5)=0.25[/tex]
[tex]f(1)=5(1)^2-2(1)=3[/tex]
[tex]f(1.5)=5(1.5)^2-2(1.5)=8.25[/tex]
[tex]f(2)=5(2)^2-2(2)=16[/tex]
[tex]f(2.5)=5(2.5)^2-2(2.5)=26.25[/tex]
[tex]f(3)=5(3)^2-2(3)=39[/tex]
Riemann sum:
[tex]\sum_{n=1}^6 f(x_n)\Delta x_n[/tex]
[tex]Sum=[f(0.5)+f(1)+f(1.5)+f(2)+f(2.5)+f(3)]\times 0.5[/tex]
[tex]Sum=[0.25+3+8.25+16+26.25+39]\times 0.5[/tex]
[tex]Sum=92.75\times 0.5[/tex]
[tex]Sum=46.375[/tex]
Therefore, the Riemann sum with n = 6 is 46.375.
