CK12 Calculus - Single Variable

and then solvefor

from whichwe get and

So the upperand lowerboundariesintersectat points and

As you can see fromthe graph, and hence and in the interval
Applyingthe area formula,
A

Integrating,

A

So the area betweenthe two curves and is

Sometimesit is possibleto applythe area formulawith respectto the -coordinatesinsteadof the -co-
ordinates.In this case,the equationsof the boundarieswill be writtenin sucha way that is expressed
explicitlyas a functionof (Figure3).