Question

find the area between the curves f(x)=e^0.8x and g(x)=-2^0.5x +1 for the interval [-3,2]

Answer 1

f(x)-g(x) sounds familiar to me

Answer 2

in other words, the height of each partition is simply the distance from f(x) to g(x)

Answer 3

can you use a calculator or all by hand?

Answer 4

i need to do it by hand

Answer 5

you will need to know which function is above and which is below.

Answer 6

Integrate top function minus the bottom function.

Answer 7

on the given interval.

Answer 8

\[\int f(x)-g(x)dx\]
no you wont, all that changes is a sign and area is always positive for drop a sign

Answer 9

\[\int_{-3}^{2} e^{0.8x}-(-2^{0.5x} +1)dx\]
hmm, might need to write that out better

Answer 10

or is that right?

Answer 11

you might wanna check to see that nothing cross tho

Answer 12

if it does then you gotta split it up at the intersection

Answer 13

does f(x)=g(x) at any point in the interval?

Answer 14

well i dont think so

Answer 15

http://www.wolframalpha.com/input/?i=f%28x%29%3De%5E%280.8x%29+and+g%28x%29%3D-2%5E%280.5x%29++%2B1%3B+x%3D-3+to+2

Answer 16

if i got your equations right, the wolf says they cross

Answer 17

i figured out the integral thing but I didn't get the answer 6.935

Answer 18

Let me say again that the graph is important.
On this interval the graphs intersect and therefore the integral must be seperated.

Answer 19

yes, intersections are important; height? not so much :)

Answer 20

(-1.282, 0.359) is the intersection right?

Answer 21

You will integrate from -3 to the point of intersection with g(x) - f(x) and then from the point of intersection to 2 with f(x)-g(x)....

Answer 22

\[\int_{-3}^{i} e^{0.8x}+2^{0.5x} -1\ dx+\int_{i}^{2} e^{0.8x}+2^{0.5x} -1\ dx\]
where i is the intersection of f and g

Answer 23

I thought you mentioned solving by hand?

Answer 24

and if one of those is negative, then toss out the "-" sign :)

Answer 25

yes I need to solve it by hand, and I did what you just said but i got the wrong answer

Answer 26

....can you show your work?

Answer 27

the wolf agrees that -1.282 is the intersect

Answer 28

That is correct....but that is not solving by hand as I stated earlier.

Answer 29

\[\int\limits_{-3}^{-1.282} -2^{0.5x}-e ^{0.8x} dx + \int\limits_{-1.282}^{2} e ^{0.8x}-(-2^{0.5x}) dx\]

Answer 30

its checking if her results are accurate tho.

Answer 31

wheres the "1"?

Answer 32

you might be better of with an exact intersect ....

Answer 33

and who is making you do this by hand?

Answer 34

its one thing to understand a concept; its another to torture ....

Answer 35

No...It is important to understand the concept and to use technology that is required in the classroom and on ap exams...

I can help her learn to enter the information into the calculator and how she must set it up by hand to write the integral that represents the area.
Dropping a sign because area is not negative is not good enough reasoning for a solution.

Answer 36

\[[-2*2^{0.5x}- 5/4e ^{0.8x}] + [5/4 e ^{0.8x}+2*2^{0.5x}]\]

Answer 37

Have a good night...

Answer 38

oh but it is; since 5-3 = 2, and 3-5 = -2 all that changes is sign, not abs value

Answer 39

oh

Answer 40

youre still missing that +1 from the top that ints up into an x

Answer 41

oh yess. I see may be that's why i dont get the answer

Answer 42

most likely :) the rest of it seems like youve got a pretty good handle on it

Answer 43

how can i forget that "1" OMG i'm so stupid

Answer 44

it happens :)

Answer 45

ok i'll try again. thank you so muchhhhhhhh and
have a great night :)