Question

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

Answer 1

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`