How do you find the Riemann sum associated with #f(x)=3x^2 +6#, n=3 and the partition of [0,6]?

1 Answer
Apr 21, 2015

Because no sample points are specified, I'll use #x_1"*", x_2"*", x_3"*"#

For #n=3#, we get #Delta x = (6-0)/3 = 2#

Ans the Sum is
#f(x_1"*")*2+f(x_2"*")*2+f(x_3"*")*2#

More simply written as
#2(f(x_1"*")+f(x_2"*")+f(x_3"*"))#

Now, if you want to show #f(x)#, write:

#2[(3(x_1"*")^2+6)+(3(x_2"*")^2+6)+(3(x_3"*")^2+6)]#

Rewrite further to taste.

Perhaps you'd prefer

#6((x_1"*")^2+(x_2"*")^2+(x_3"*")^2)+36#