Problem :
What is the relationship between
f (x)dx and f (x)dx?
Since
f (x)dx
= F(b) - F(a), and
f (x)dx
= F(a) - F(b),
f (x)dx
= - f (x)dx
Problem :
For the function graphed below, find
f (x)dx
f (x)dx
f (x)dx
Recall the interpretation of the definite integral as the signed area under the curve.
Portions below the graph count as "negative area" even though such a thing could not
exist geometrically.