### Home > CALC > Chapter 4 > Lesson 4.2.1 > Problem 4-50

4-50.

If 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 represents the infinitely small width of each rectangle.

Now let’s find the height of each rectangle.

Heights, of course, are represented by a function,

*.*

But what is

*?*

Since is a variable, we will let

*represent the part of the series that is changing:*

This is beginning to look more like an integral:

We still need to find the bounds of the integral.

The lowest value of