Original
Let {{MATH_7}} be the constant function {{MATH_8}}. Let {{MATH_9}} be any antiderivative
of {{MATH_10}}. Then {{MATH_11}}.
{{CMD_12}}
This is just a fancy way of saying that {{MATH_13}} is a line of slope
{{MATH_14}}, and we are looking for the rise corresponding to a run of
{{MATH_15}}
{{CMD_16}}
{{CMD_17}}
{{MATH_18}}
{{CMD_19}}
{{CMD_20}}
{{CMD_21}}
The area of the region bounded by the graph of {{MATH_22}}, the horizontal
axis, and the vertical lines {{MATH_23}} and {{MATH_24}} is {{MATH_25}}.
{{CMD_26}}
{{CMD_27}}
{{ENV_28}}
{{CMD_29}}
{{CMD_30}}
{{CMD_31}}
This is a rectangle with height {{MATH_32}} and width {{MATH_33}}, so the area is {{MATH_34}}
{{CMD_35}}
{{CMD_36}}