## anonymous 4 years ago find the area between the curves f(x)=e^0.8x and g(x)=-2^0.5x +1 for the interval [-3,2]

1. amistre64

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

2. amistre64

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

3. anonymous

can you use a calculator or all by hand?

4. amistre64

|dw:1327280743692:dw|

5. anonymous

i need to do it by hand

6. anonymous

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

7. anonymous

Integrate top function minus the bottom function.

8. anonymous

on the given interval.

9. 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

10. amistre64

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

11. amistre64

or is that right?

12. amistre64

you might wanna check to see that nothing cross tho

13. amistre64

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

14. amistre64

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

15. anonymous

well i dont think so

16. amistre64
17. amistre64

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

18. anonymous

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

19. anonymous

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

20. amistre64

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

21. anonymous

(-1.282, 0.359) is the intersection right?

22. 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)....

23. 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

24. anonymous

I thought you mentioned solving by hand?

25. amistre64

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

26. anonymous

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

27. anonymous

28. amistre64

the wolf agrees that -1.282 is the intersect

29. anonymous

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

30. anonymous

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

31. amistre64

its checking if her results are accurate tho.

32. amistre64

wheres the "1"?

33. amistre64

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

34. amistre64

and who is making you do this by hand?

35. amistre64

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

36. 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.

37. anonymous

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

38. anonymous

Have a good night...

39. amistre64

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

40. anonymous

oh

41. amistre64

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

42. anonymous

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

43. amistre64

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

44. anonymous

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

45. amistre64

it happens :)

46. anonymous

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