Original
Recall: {{MATH_10}}.
{{CMD_11}}
{{ENV_12}}
{{CMD_13}}
Recall: {{MATH_14}}
{{CMD_15}}
{{CMD_16}}
Recall: {{MATH_17}}. Determine the value {{MATH_18}} from the graph.
{{CMD_19}}
For {{MATH_20}}, we can express {{MATH_21}} as
{{MATH_22}}
{{CMD_23}}
Recall: {{MATH_24}} for {{MATH_25}}.
{{CMD_26}}
{{CMD_27}}
Recall: {{MATH_28}} for {{MATH_29}}. {{MATH_30}} is a linear function on the interval {{MATH_31}}.
{{CMD_32}}
For {{MATH_33}}, we can experss {{MATH_34}} as
{{MATH_35}}
{{CMD_36}}
Recall: {{MATH_37}} for {{MATH_38}}. This definite integral gives signed area of the region between the graph of {{MATH_39}} and the interval {{MATH_40}} on the {{MATH_41}}axis.
This region is a triangle with the base {{MATH_42}} and the height {{MATH_43}}. Compute the area of the triangle!
{{CMD_44}}
{{MATH_45}}
{{CMD_46}}
This integral gives the area of the region between the graph of {{MATH_47}} and the interval {{MATH_48}} on the {{MATH_49}}axis. Use geometry!
It can be expressed as {{MATH_50}}.
{{CMD_51}}
{{CMD_52}}
{{CMD_53}}