9.3 #17

[Chris Moss]

What does it mean to do the problem graphically? How are we supposed
to represent the integral as an area without first doing calculus to
explain it?


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[Professor Laugesen]

Right, the key point is that the integral represents area.
So sketch a graph of some even function, and use your sketch to
explain the formula. There is no need to do any actual calculation.
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What I want to encourage, on this problem, is thinking about what the
formula means in terms of areas. (What I want to discourage is proving
it by a change of variable with no understanding of what the formula
means!)