## anonymous 4 years ago Consider the function f(x) = 2sin(x2) on the interval 0 ≤ x ≤ 3. (a) Find the exact value in the given interval where an antiderivative, F, reaches its maximum. x = (b) If F(1) = 9, estimate the maximum value attained by F. (Round your answer to three decimal places.) y ≈

1. inkyvoyd

set 2sin(x^2)=0

2. inkyvoyd

Wait, over an interval -_-

3. inkyvoyd

Ignore the interval, and just solve that trig equation.

4. anonymous

i know that the answer for part "a" is

5. anonymous

square(pi)

6. inkyvoyd

square or sqrt?

7. anonymous

i dont know how to do part b

8. anonymous

sqrt

9. inkyvoyd

Well, your interval s defined only up to 3. Is that supposed to be that way, or is the three suposed to be pi?

10. anonymous

up to 3

11. anonymous

a)$2*\sin(2*x)=0\rightarrow x=k*pi/2$ In this interval x=pi/2

12. inkyvoyd

Do you understand a though?

13. anonymous

well i got x= |dw:1334814197335:dw|

14. inkyvoyd

|dw:1334814169184:dw|

15. anonymous

16. inkyvoyd

|dw:1334814236680:dw|

17. inkyvoyd

Naturally, sqrt pi would be the largest value up to 3, because it squares out to pi.

18. anonymous

the equation is f(x) = 2sin(x^2)

19. anonymous

20. anonymous

$F(x)=-\cos(2*x)+K'$ $F(1)=-\cos(2*1)+K'=9$

21. inkyvoyd

I know - That is sin x

22. inkyvoyd

but, sin x^2 is similar to the graph in that it has its highest values at sqrtpi

23. anonymous

sqrt(pi) is the right answer for part a is marking it right

24. anonymous

the part that i dont get how to do is part b

25. inkyvoyd

Yes. Can you tell me what calc course you are enrolled in?

26. anonymous

calculus I

27. inkyvoyd

Alright, give me a second.

28. anonymous

2sin(x^2) = 0 x^2 = pi x = sqrt(pi)

29. anonymous

thats how i got my answer

30. inkyvoyd

Have you learned how to approximate integrals?

31. anonymous

kinda

32. anonymous

thats what we are learning

33. inkyvoyd

What's it called?

34. anonymous

antiderivatives

35. inkyvoyd

No, what kind of approximations have you learned?

36. inkyvoyd

I just figured out how I can solve the problem.

37. inkyvoyd

Here's the graph, btw

38. anonymous

i dont know

39. inkyvoyd
40. anonymous

the tittle of this chapter is antiderivatives

41. inkyvoyd

Note how the function uses something called the fresnal S, which I don't know either. But mor eimportantly, notice how it gets to its peak at about 1,7

42. anonymous

so how do i do part b?

43. inkyvoyd

I'm thinking ;)

44. inkyvoyd

Have you learned trapozoidal approximation?

45. anonymous

no

46. anonymous

I also have a question for part b... help us figure this out plz

47. inkyvoyd
48. inkyvoyd

Alright. that is the graph of f(x)=2 sin(x^2) right?

49. inkyvoyd

Notice how the waves become wider and wider close to 0.

50. inkyvoyd

after that, they become thinner and thinner.

51. inkyvoyd

Now, give me a second to explain something.

52. inkyvoyd

Let me get htis plot into mathematica, and show you what I'm talking about.

53. anonymous

k

54. inkyvoyd

55. inkyvoyd

Ok. The area of a>b>c>d Tell me if you understand.

56. inkyvoyd

@Ldaniel ?

57. anonymous

yes i do

58. inkyvoyd

So, because of this, we know that from 0 to 3, the area enclosed in a is the greatest

59. anonymous

yes

60. inkyvoyd

So we are essentially looking for the area there.

61. inkyvoyd

@FoolForMath , I give up/

62. anonymous

;/

63. inkyvoyd

I can give you the answer though, me being a cheater cheater.

64. anonymous

65. anonymous

i wish i could do this math. -_-

66. inkyvoyd

Give me a second.

67. inkyvoyd

I'm going to numerically evaluate the integral with wolfram Mathematica

68. inkyvoyd

1.78966

69. inkyvoyd

@lgbasallote , here you go.

70. anonymous

71. inkyvoyd

WHAT?

72. inkyvoyd

Try the square root of pi then.

73. anonymous

74. inkyvoyd

Yes.

75. anonymous

wrong

76. inkyvoyd

btw, try 1.790 if you haven't already.

77. anonymous

i did its wrong

78. inkyvoyd

Ahem.

79. anonymous

;(

80. anonymous

lol why call me =)) i only know algebra :P i dont like these stuffs

81. anonymous

:((

82. inkyvoyd

Wrong, call >.<

83. inkyvoyd
84. inkyvoyd

So, you are supposed to use an estimation method that isn't accurate, nor do I know. Or, the problem is set up funy.

85. inkyvoyd

86. inkyvoyd

If I used the methods they gave, I might just get the answer they are looking for.

87. anonymous

i got the answer is y = 10.16912...

88. inkyvoyd

89. anonymous

|dw:1334818371099:dw|

90. anonymous

yes

91. anonymous

so$\int\limits_{1}^{\sqrt{\pi}}f(x) = F(\sqrt{\pi}) - F(1)$ all you need to do is find approximation for definite integral

92. inkyvoyd

Well, then I'm completely useless.

93. anonymous

94. inkyvoyd

Nice job.

95. anonymous

thanks anyways

96. anonymous

how old are you?

97. inkyvoyd

15

98. inkyvoyd

I'm still not sure how I missed that problem so badly. :/

99. anonymous

15? really?

100. anonymous
101. anonymous

yes dumbcow

102. anonymous

sorry for being redundant, i know you already got the answer just putting it out there for everyones benefit

103. anonymous

I believe graph would go like this. (the pitch decreasing with increase in x) |dw:1334819574505:dw|

104. inkyvoyd

btw, yes, I'm trying to jump the gun and finish calculus and some math afterwards before I enter college.