Let f(x) = 3x(4 - x)
Suppose we partition the interval [1; 3] into n subintervals of equal length, and then use the right-hand endpoints of these subintervals as sample points. Find an expression for the corresponding Riemann sum for f(x).
Let f(x) = 3x(4 - x)
Suppose we partition the interval [1; 3] into n subintervals of equal length, and then use the right-hand endpoints of these subintervals as sample points. Find an expression for the corresponding Riemann sum for f(x).
The interval has length units. If you divide it into subintervals, then the length of each subinterval is . This is the length of each rectangle.
The width of each rectangle will be for (since you are taking the right hand endpoints you don't use ).
So that means each rectangle's area is
.
The total area therefore is
By making , the area of the rectangles converges on the area underneath the curve.