### Home > CALC > Chapter Ch2 > Lesson 2.1.3 > Problem 2-40

2-40.

Recall problem 2-17:

i. For left-endpoint and midpoint rectangles, let the index start at 0 and end at *n*-1.

For right-endpoint rectangles, let the index start at 1 and end at *n*. *n* = number of rectangles.

To determine the width of each rectangle, divide the domain by the number of rectangles:

iii. The transformed function represents the HEIGHT of each rectangle.

For left- and right-endpoint rectangles, the heights are represented by *f*(*a* + Δ*xi*).

For midpoint rectangles, the heights are represented by

*a* = starting value

Δ*x* = width of each rectangle.