If n is a positive integer write an integral to represent
Notice that this is a Riemann sum with infinitely many rectangles.
And a Riemann sum with infinitely many rectangles is the Definition of an Integral:
Can you rewrite this as an integral?
The dx represents the infinitely small width of each rectangle.
Now lets find the height of each rectangle.
Heights, of course, are represented by a function, f(x).
But what is f(x)?
Since x is a variable, we will let x represent the part of the series that is changing:
We still need to find the bounds of the integral.