Individual Project ~ FRQ Presentation

2002 AP Calculus AB #1

Marija Jevtic

There are no points of

intersection, but we are

given an interval from

to x = 1

In order to find the area

of a region enclosed by

two graphs, we must use

the following formula

where f(x) represents

the upper

function ,

and g(x) represents the

lower function ,

a is the upper limit ( )

b is the lower limit (1)

The answer, when the equation is plugged in the

calculator is 1.22

y = 4

In order to find the volume of the solid revolved around y = 4

we must use the Washer Method

R =

r =

When all the information is plugged into the formula, we get:

The R and r are determined in accordance to the line around which the

graph revolves (y = 4). R is the outer ring (further from the line), while r

is the inner ring, meaning that it is closer to the given line. Also, the

specific line must be included in the formula if it is anything but y = 0.

Answer: 23.609

First find the derivative of h(x)

and set it equal to zero in order

to find the critical values

An absolute minimum and

maximum occur at either the

critical point or at one of the

endpoints, meaning we must

find h(x) values for all of them

and test which is the lowest one

x = 0.567143

x h(x)

1/2

0.567143

1

Absolute minimum value:

h(0.567143) = 2.330

Absolute maximum value:h(1) = 2.718

References

• www.collegeboard.org• www.mszhao.com• www.deviantart.com• Microsoft Word (for equations)• http://www.mathsrev.com/graph-of-yln-x-and-graph-of-yex/

THANK YOU!Hope you enjoyed!