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

- anonymous

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

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- amistre64

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

- amistre64

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

- anonymous

can you use a calculator or all by hand?

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## More answers

- amistre64

|dw:1327280743692:dw|

- anonymous

i need to do it by hand

- anonymous

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

- anonymous

Integrate top function minus the bottom function.

- anonymous

on the given interval.

- amistre64

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

- amistre64

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

- amistre64

or is that right?

- amistre64

you might wanna check to see that nothing cross tho

- amistre64

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

- amistre64

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

- anonymous

well i dont think so

- amistre64

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

- amistre64

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

- anonymous

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

- anonymous

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

- amistre64

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

- anonymous

(-1.282, 0.359) is the intersection right?

- anonymous

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)....

- amistre64

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

- anonymous

I thought you mentioned solving by hand?

- amistre64

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

- anonymous

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

- anonymous

....can you show your work?

- amistre64

the wolf agrees that -1.282 is the intersect

- anonymous

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

- anonymous

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

- amistre64

its checking if her results are accurate tho.

- amistre64

wheres the "1"?

- amistre64

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

- amistre64

and who is making you do this by hand?

- amistre64

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

- anonymous

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.

- anonymous

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

- anonymous

Have a good night...

- amistre64

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

- anonymous

oh

- amistre64

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

- anonymous

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

- amistre64

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

- anonymous

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

- amistre64

it happens :)

- anonymous

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

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