anonymous
  • anonymous
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 ≈
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
inkyvoyd
  • inkyvoyd
set 2sin(x^2)=0
inkyvoyd
  • inkyvoyd
Wait, over an interval -_-
inkyvoyd
  • inkyvoyd
Ignore the interval, and just solve that trig equation.

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More answers

anonymous
  • anonymous
i know that the answer for part "a" is
anonymous
  • anonymous
square(pi)
inkyvoyd
  • inkyvoyd
square or sqrt?
anonymous
  • anonymous
i dont know how to do part b
anonymous
  • anonymous
sqrt
inkyvoyd
  • 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?
anonymous
  • anonymous
up to 3
anonymous
  • anonymous
a)\[2*\sin(2*x)=0\rightarrow x=k*pi/2\] In this interval x=pi/2
inkyvoyd
  • inkyvoyd
Do you understand a though?
anonymous
  • anonymous
well i got x= |dw:1334814197335:dw|
inkyvoyd
  • inkyvoyd
|dw:1334814169184:dw|
anonymous
  • anonymous
and is the right answer
inkyvoyd
  • inkyvoyd
|dw:1334814236680:dw|
inkyvoyd
  • inkyvoyd
Naturally, sqrt pi would be the largest value up to 3, because it squares out to pi.
anonymous
  • anonymous
the equation is f(x) = 2sin(x^2)
anonymous
  • anonymous
sorry about that
anonymous
  • anonymous
\[F(x)=-\cos(2*x)+K'\] \[F(1)=-\cos(2*1)+K'=9\]
inkyvoyd
  • inkyvoyd
I know - That is sin x
inkyvoyd
  • inkyvoyd
but, sin x^2 is similar to the graph in that it has its highest values at sqrtpi
anonymous
  • anonymous
sqrt(pi) is the right answer for part a is marking it right
anonymous
  • anonymous
the part that i dont get how to do is part b
inkyvoyd
  • inkyvoyd
Yes. Can you tell me what calc course you are enrolled in?
anonymous
  • anonymous
calculus I
inkyvoyd
  • inkyvoyd
Alright, give me a second.
anonymous
  • anonymous
2sin(x^2) = 0 x^2 = pi x = sqrt(pi)
anonymous
  • anonymous
thats how i got my answer
inkyvoyd
  • inkyvoyd
Have you learned how to approximate integrals?
anonymous
  • anonymous
kinda
anonymous
  • anonymous
thats what we are learning
inkyvoyd
  • inkyvoyd
What's it called?
anonymous
  • anonymous
antiderivatives
inkyvoyd
  • inkyvoyd
No, what kind of approximations have you learned?
inkyvoyd
  • inkyvoyd
I just figured out how I can solve the problem.
inkyvoyd
  • inkyvoyd
Here's the graph, btw
anonymous
  • anonymous
i dont know
inkyvoyd
  • inkyvoyd
http://www.wolframalpha.com/input/?i=integrate+2+sin%28x%5E2%29
anonymous
  • anonymous
the tittle of this chapter is antiderivatives
inkyvoyd
  • 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
anonymous
  • anonymous
so how do i do part b?
inkyvoyd
  • inkyvoyd
I'm thinking ;)
inkyvoyd
  • inkyvoyd
Have you learned trapozoidal approximation?
anonymous
  • anonymous
no
anonymous
  • anonymous
I also have a question for part b... help us figure this out plz
inkyvoyd
  • inkyvoyd
http://www.wolframalpha.com/input/?i=+2+sin%28x%5E2%29
inkyvoyd
  • inkyvoyd
Alright. that is the graph of f(x)=2 sin(x^2) right?
inkyvoyd
  • inkyvoyd
Notice how the waves become wider and wider close to 0.
inkyvoyd
  • inkyvoyd
after that, they become thinner and thinner.
inkyvoyd
  • inkyvoyd
Now, give me a second to explain something.
inkyvoyd
  • inkyvoyd
Let me get htis plot into mathematica, and show you what I'm talking about.
anonymous
  • anonymous
k
inkyvoyd
  • inkyvoyd
1 Attachment
inkyvoyd
  • inkyvoyd
Ok. The area of a>b>c>d Tell me if you understand.
inkyvoyd
  • inkyvoyd
@Ldaniel ?
anonymous
  • anonymous
yes i do
inkyvoyd
  • inkyvoyd
So, because of this, we know that from 0 to 3, the area enclosed in a is the greatest
anonymous
  • anonymous
yes
inkyvoyd
  • inkyvoyd
So we are essentially looking for the area there.
inkyvoyd
  • inkyvoyd
@FoolForMath , I give up/
anonymous
  • anonymous
;/
inkyvoyd
  • inkyvoyd
I can give you the answer though, me being a cheater cheater.
anonymous
  • anonymous
what's the answer?
anonymous
  • anonymous
i wish i could do this math. -_-
inkyvoyd
  • inkyvoyd
Give me a second.
inkyvoyd
  • inkyvoyd
I'm going to numerically evaluate the integral with wolfram Mathematica
inkyvoyd
  • inkyvoyd
1.78966
inkyvoyd
  • inkyvoyd
@lgbasallote , here you go.
anonymous
  • anonymous
the answer is wrong
inkyvoyd
  • inkyvoyd
WHAT?
inkyvoyd
  • inkyvoyd
Try the square root of pi then.
anonymous
  • anonymous
as the answer?
inkyvoyd
  • inkyvoyd
Yes.
anonymous
  • anonymous
wrong
inkyvoyd
  • inkyvoyd
btw, try 1.790 if you haven't already.
anonymous
  • anonymous
i did its wrong
inkyvoyd
  • inkyvoyd
Ahem.
anonymous
  • anonymous
;(
lgbasallote
  • lgbasallote
lol why call me =)) i only know algebra :P i dont like these stuffs
anonymous
  • anonymous
:((
inkyvoyd
  • inkyvoyd
Wrong, call >.<
inkyvoyd
  • inkyvoyd
http://www.wolframalpha.com/input/?i=integral%5B2+sin%28x%5E2%29%2C%7Bx%2C0%2Csqrt%28pi%29%7D%5D
inkyvoyd
  • 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.
inkyvoyd
  • inkyvoyd
Got any more info about what you are learning right now?
inkyvoyd
  • inkyvoyd
If I used the methods they gave, I might just get the answer they are looking for.
anonymous
  • anonymous
i got the answer is y = 10.16912...
inkyvoyd
  • inkyvoyd
That's th correct answer?
anonymous
  • anonymous
|dw:1334818371099:dw|
anonymous
  • anonymous
yes
dumbcow
  • dumbcow
so\[\int\limits_{1}^{\sqrt{\pi}}f(x) = F(\sqrt{\pi}) - F(1)\] all you need to do is find approximation for definite integral
inkyvoyd
  • inkyvoyd
Well, then I'm completely useless.
anonymous
  • anonymous
10.170 is the answer
inkyvoyd
  • inkyvoyd
Nice job.
anonymous
  • anonymous
thanks anyways
anonymous
  • anonymous
how old are you?
inkyvoyd
  • inkyvoyd
15
inkyvoyd
  • inkyvoyd
I'm still not sure how I missed that problem so badly. :/
anonymous
  • anonymous
15? really?
dumbcow
  • dumbcow
http://www.wolframalpha.com/input/?i=integrate+2sin%28x^2%29+dx+from+1+to+sqrt%28pi%29 add 9 to get answer
anonymous
  • anonymous
yes dumbcow
dumbcow
  • dumbcow
sorry for being redundant, i know you already got the answer just putting it out there for everyones benefit
apoorvk
  • apoorvk
I believe graph would go like this. (the pitch decreasing with increase in x) |dw:1334819574505:dw|
inkyvoyd
  • inkyvoyd
btw, yes, I'm trying to jump the gun and finish calculus and some math afterwards before I enter college.

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