Sure! To find the Riemann sum of the function 1+x^2 on the interval [0,1], we need to first divide the interval into smaller subintervals and calculate the value of the function at each partition point.
Let's say we want to divide the interval into n subintervals. The length of each subinterval will be Δx = (1-0)/n = 1/n.
Now, we need to choose one point from each subinterval to evaluate the function. We can choose the midpoint of each subinterval as the evaluation point.
So, the evaluation points will be x_i = (0 + Δx/2) + iΔx, where i ranges from 0 to n-1.
Now, we can calculate the value of the function at each evaluation point and multiply it by the length of the subinterval.
The Riemann sum is calculated by summing all these products:
Riemann Sum = Σ (1 + x_i^2) * Δx
Where Σ represents the sum and i ranges from 0 to n-1.
I hope this helps you find the Riemann sum of the function 1+x^2 on the interval [0,1]. If you have any other questions, feel free to ask!