Original
Compute the average value of the function
{{MATH_156}}
on the interval {{MATH_157}}.
{{CMD_158}}
By definition, we wish to compute
{{MATH_159}}
Computing this integral geometrically, we find the average value
to be {{MATH_160}}.
{{CMD_161}}
{{CMD_162}}
Another way we can make sense of ``The average height of a point on the
unit semi circle'' is the average value of the function
{{MATH_163}}
on {{MATH_164}}, since {{MATH_165}} is the height of the point on the
unit circle at the angle {{MATH_166}}.
{{CMD_167}}
Compute the average value of the function
{{MATH_168}}
on the interval {{MATH_169}}.
{{CMD_170}}
By definition, we wish to compute
{{MATH_171}}
Computing this integral geometrically, we find the average value
to be {{MATH_172}}.
{{CMD_173}}
{{CMD_174}}