Question

Write the Riemann sum to find the area under the graph of the function f(x) = x^2 from x = 1 to x = 5.

Answer 1

Let \(P :=\{1=x_0, x_2,......,x_n=5\}\) be a partition of [1,5]
then Riemann sum of f(x) is
\[\sum_{i=1}^n f(x^*_i )(x_{i+1}-x_i)\]

Answer 2

So would it be the first or second one?
\[\sum_{i=1}^{n}(1+(5i)/n)^2(4/n)\]

\[\sum_{i=1}^{n}(4i/n)^2(4/n)\]

Answer 3

first right?

Answer 4

@Loser66

Answer 5

I think so