## Jaweria 2 years ago I need help with one question of Calculus 1.

1. dave0616

2. Jaweria

My question is this: USe 5 rectangles to estimate the area under the graph of: f(x) = 2x^3+2x-5. from x=2 to x=7

3. Jaweria

And also tell whether your estimate is an over or an upper estimate, explain why?

4. dave0616

oh you are doing reimann sums? let me do some work, give me a second

5. Jaweria

ok thx

6. Jaweria

if you can check with me that I got my 5 rectangles: 35, 93, 193, -92, -128 are they right?

7. dave0616

hmmmmm im gonna draw up the graph so that we know we have the same thing|dw:1366346945142:dw| That is the graph that i have, roughly at least, is that the same thing that you are working with?

8. Jaweria

yeah

9. Jaweria

but can you please check my numbers plzz

10. dave0616

i punched this into my calculator, and the base for each rectangle would be 1, because you are using 5 rectangles, and the difference between 7 and 2 is 5. so you are basicallly looking at the height, but i got 15, 55, 131, 255, and 439. i dont see how you could get any negative because the line is going up

11. Jaweria

yeah i got that too but I m saying that arent we suppose to add up those rectangles?

12. Jaweria

13. Jaweria

Someone plzz help me

14. jojo921

intervals =b-a/n (7-2)/5 =1

15. dave0616

yea, you just add what you got for the areas, so 15+55+131+255+439=839. and it would be an under estimate because it is a left side reimann sum. meaning that the left corner of the boxes hit the line

16. Jaweria

i thought its over estimate because its increasing

17. dave0616

|dw:1366348904077:dw| that isnt to scale, but that is the basic idea of what is going on

18. Jaweria

oh thx

19. dave0616

no problem

20. Jaweria

one more plzz

21. dave0616

shoot

22. Jaweria

if you dont mind

23. Jaweria

ok

24. Jaweria

Use 5 rectangles to esitmate the area under the graph: y=x^3-10x^2+27x-18

25. Jaweria

from 1<equal to x <equalt to 6

26. Jaweria

|dw:1366349539104:dw|

27. dave0616

ok so your graph is going to look like: |dw:1366349701319:dw| roughly of course.

28. Jaweria

its ok

29. Jaweria

so how am I actually going to solve this

30. dave0616

are you supposed to use 5 boxes again?

31. Jaweria

yeah its says 5 rectangles

32. dave0616

does this problem have the same basis as the other problem you posted? meaning you are just looking for rectangles to find the area under the graph? ok, 5 rectangles

33. Jaweria

yeah

34. Jaweria

and it also gives you from where to where

35. Jaweria

which is this |dw:1366349945211:dw|

36. dave0616

right, so this again is the same difference as the other problem, (5) so each will have the same base length of 1

37. Jaweria

ok

38. Jaweria

can we work on this together little bit ?

39. Jaweria

If you dont mind?

40. dave0616

yes of course we can. how would you like to do that? i would like to help you in the best way that suits you

41. Jaweria

can you first show me how to get the value for the 1st rectangle?

42. dave0616

yes, i personally am using a graphing calculator because i find it is the easiest way to do it. are you using the same, or are you trying to do this by hand?

43. dave0616

@Jaweria

44. Jaweria

hand

45. Jaweria

we are not allow to use calculator

46. dave0616

ok, that is fine, that just means that we are going to have to find the value for y at every point. and our points are going to be 1,2,3,4,5,6. do you think you can solve for y using the equation for these six points? and would you like to solve them on your own, and then post them, and we can compare values?

47. Jaweria

ok so first I m using 1 for my y

48. dave0616

nope, we are gonna be solving for y, so we are going to plug 1,2,3,4,5 and 6 in for x into the equation

49. Jaweria

oh ok

50. dave0616

so solve for y, using those six values and let me know what you get

51. Jaweria

so let me get their values then I ll tell you

52. Jaweria

alright

53. dave0616

ok, and solve for 1,2,3,4,5 that will give us 5 rectangles

54. dave0616

did you get the values?

55. Jaweria

so far I got 10,4,0

56. dave0616

hmmmm, that first one isnt correct try it again

57. Jaweria

ok

58. Jaweria

its 0

59. dave0616

that is correct, now go ahead and fine the y value for 4 and 5

60. Jaweria

ok

61. dave0616

did you solve for them? sorry if i am rushing you, i dont mean to be

62. dave0616

@jaweria

63. Jaweria

I m sorry my stupid laptop is giving me tough time

64. dave0616

its all good no worries

65. Jaweria

I got -10

66. Jaweria

is that right?

67. dave0616

you need, two more values, but -10 is not correct, you are going to need to solve for 4 and 5. go ahead and do that and let me know what you get

68. Jaweria

I got -6 for 4

69. Jaweria

and -8 for 5

70. dave0616

that is correct. now we need to find the area of each of those rectangles. and the base of each of those rectangles is 1, so the area of each of those rectangles will be equal to the value, so we have 0,4,0,-6,-8. so now all we need to do is add those values.

71. dave0616

so A=0+4+0-6-8. what do you get for area?

72. Jaweria

yeah i got that too all of them

73. Jaweria

but then how am i suppose to find an area add them up?

74. Jaweria

and then divide it by some number?

75. dave0616

we found that the base of each of those rectangles would be 1. and the area of a rectangle is b*h. we found the height by finding the y. so in essence you are multplying each of the values we found (0,4,0,-6,-8) by one, but they will equal the values themselves. so what wer are actually doing is A=0(1)+4(1)+0(1)-6(1)-8(1)

76. dave0616

can you solve for area from that?

77. Jaweria

oh ok

78. dave0616

what do you get for area?

79. Jaweria

yeah its -10

80. Jaweria

I m still getting -10

81. dave0616

thta is right. is that what you were reffering to earlier when you said -10?

82. Jaweria

yup

83. dave0616

oh im extremely sorry, i did not realize that is what you were referrring to. i really do feel bad, im sorry. but yes it is -10, and it would still be an under estimate because we used a left corner triangle

84. Jaweria

its ok :)

85. Jaweria

86. dave0616

haha ok. well im glad we went through it still. yes the area under the graph by the estimate of 5 rectangles is -10. do you understand how we came to the answer?

87. Jaweria

yup I completely did thanks a lot:)

88. dave0616

absolutely no problem!

89. Jaweria

I should go to sleep now its really late take care bye.

90. dave0616

i hear ya haha. take care and good luck in your studies