## anonymous one year ago The base of a solid is bounded by the curve y = sqrt(x + 1), the x-axis and the line x = 1. The cross sections, taken perpendicular to the x-axis, are squares. Find the volume of the solid 1 2 2.333 None of these

1. anonymous

@freckles @ganeshie8 @Hero @nincompoop @Robert136 @satellite73

2. anonymous

2, I think.

3. anonymous

dont really want the answer as much as i want to know how to do it :P

4. triciaal

5. rds8701

PLEASE HELP WILL FAN AND MEDAL According to an article in Runners' World magazine: On average the human body is more than 50 percent water [by weight]. Runners and other endurance athletes average around 60 percent. This equals about 120 soda cans' worth of water in a 160-pound runner! Investigate their calculation. Approximately how many soda cans’ worth of water are in the body of a 160-pound runner? What unprovided information do you need to answer this question?

6. anonymous

wingspan move man ... wingspan move.

7. triciaal

I think we need the area under the curve between 0 and 1 times the height

8. SolomonZelman

Is the region bounded by sqrt(x+1), y=0, and x=1 rotated around some line? Because without that, so far, you only have a 2D object....

9. triciaal

|dw:1439477813129:dw|

10. anonymous

its not rotated its |dw:1439477867812:dw| this is what it should loo like

11. triciaal

when y = 0 then x = -1

12. anonymous

i don't really see how that's useful

13. triciaal

did you see the graph?

14. anonymous

yes i have a ti-84 iv graphed it , i have a table of values, don't see the use to it though

15. SolomonZelman

Never claimed to be good at math, but to me the question is missing, because as it is the very region you are dealing with is 2D.

16. anonymous

pretty sure that its a complete question and that the object described is 3d

17. anonymous

@ParthKohli @OregonDuck any ideas ?

18. SolomonZelman

It is just bound by some (explicit) functions, and there is no reason for it to be 3D. Is it rotated about some line? You said it is not.

19. anonymous

it says that the cross sections perpendicular to the x axis are squares, only 3d objects have cross sections

20. triciaal

so we need the integral between -1 and 1

21. anonymous

22. anonymous

@pooja195

23. triciaal

we have half a parabola that opens right guess none of the above

24. freckles

|dw:1439482917191:dw|

25. freckles

|dw:1439483111182:dw| I'm bad about drawing 3d objects but this is what the shape looks like

26. freckles

sorta

27. freckles

|dw:1439483183181:dw|

28. freckles

@jdosio do you see how to setup the integral let me know when you get back on

29. freckles

in other words you need to find the area of the square

30. freckles

and use that as the integrand

31. IrishBoy123
32. anonymous

damn now your offline, ill be on for the remainder of the day @freckles tell me when you get back on

33. anonymous

also thats the only part i have a problem with,(setting up the integral ) i know what the solid looked like and all just not sure how to calculate its volume

34. freckles

$V=\int\limits_{-1}^1 A(x) dx \\ \text{ where } A(x)=\text{ area of square }$ |dw:1439494770565:dw|

35. freckles

$A(x)=\text{ area of square}=\text{ height } ^2$

36. freckles

the integrand is just x+1 that is A(x)=x+1

37. freckles

$V=\int\limits_{-1}^1 (x+1) dx$

38. anonymous

isint it $\sqrt{x+1}$

39. freckles

that is the height you also have the base is that too the area of a square=base*height or height^2 since base=height

40. freckles

|dw:1439495278485:dw| if that length here is sqrt(x+1) then the base length of that shape is also sqrt(x+1) since the shape is a square

41. freckles

|dw:1439495315876:dw|

42. freckles

$A(x)=\sqrt{x+1} \cdot \sqrt{x+1}=(x+1)$

43. anonymous

!! i get it !!

44. freckles

notice the lower limit is x=-1 and the upper limit is x=1

45. freckles

$V=\int\limits _{-1}^1 A(x) dx \\ A(x)=\sqrt{x+1} \cdot \sqrt{x+1}=x+1 \\ V=\int\limits_{-1}^{1} (x+1) dx$ V represents the volume by the way

46. anonymous

okay im getting 2

47. freckles

sounds great that is what @IrishBoy123 got using double integrals

48. anonymous

thanks for your help freckles , cant thank you enough