Original
Consider {{MATH_165}}. Approximate the area between the graph of {{MATH_166}} and
the {{MATH_167}}-axis on the interval {{MATH_168}} using a {{CMD_169}}right-endpoint{{CMD_170}} Riemann
sum with {{MATH_171}} rectangles.
{{CMD_172}}
First note that the width of each rectangle is
{{MATH_173}}
The grid points define the edges of the rectangle and are seen below:
{{CMD_174}}
{{ENV_175}}
{{CMD_176}}
On the other hand, the sample points identify which endpoints we use:
{{CMD_177}}
{{ENV_178}}
{{CMD_179}}
It is helpful to collect all of this data into a table:
{{MATH_180}}
Now we may write a right Riemann sum
{{MATH_181}}
which evaluates to
{{ENV_182}}
and we find
{{MATH_183}}
{{CMD_184}}
{{CMD_185}}