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 ≈

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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
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set 2sin(x^2)=0
Wait, over an interval -_-
Ignore the interval, and just solve that trig equation.

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Other answers:

i know that the answer for part "a" is
square(pi)
square or sqrt?
i dont know how to do part b
sqrt
Well, your interval s defined only up to 3. Is that supposed to be that way, or is the three suposed to be pi?
up to 3
a)\[2*\sin(2*x)=0\rightarrow x=k*pi/2\] In this interval x=pi/2
Do you understand a though?
well i got x= |dw:1334814197335:dw|
|dw:1334814169184:dw|
and is the right answer
|dw:1334814236680:dw|
Naturally, sqrt pi would be the largest value up to 3, because it squares out to pi.
the equation is f(x) = 2sin(x^2)
sorry about that
\[F(x)=-\cos(2*x)+K'\] \[F(1)=-\cos(2*1)+K'=9\]
I know - That is sin x
but, sin x^2 is similar to the graph in that it has its highest values at sqrtpi
sqrt(pi) is the right answer for part a is marking it right
the part that i dont get how to do is part b
Yes. Can you tell me what calc course you are enrolled in?
calculus I
Alright, give me a second.
2sin(x^2) = 0 x^2 = pi x = sqrt(pi)
thats how i got my answer
Have you learned how to approximate integrals?
kinda
thats what we are learning
What's it called?
antiderivatives
No, what kind of approximations have you learned?
I just figured out how I can solve the problem.
Here's the graph, btw
i dont know
http://www.wolframalpha.com/input/?i=integrate+2+sin%28x%5E2%29
the tittle of this chapter is antiderivatives
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
so how do i do part b?
I'm thinking ;)
Have you learned trapozoidal approximation?
no
I also have a question for part b... help us figure this out plz
http://www.wolframalpha.com/input/?i=+2+sin%28x%5E2%29
Alright. that is the graph of f(x)=2 sin(x^2) right?
Notice how the waves become wider and wider close to 0.
after that, they become thinner and thinner.
Now, give me a second to explain something.
Let me get htis plot into mathematica, and show you what I'm talking about.
k
1 Attachment
Ok. The area of a>b>c>d Tell me if you understand.
yes i do
So, because of this, we know that from 0 to 3, the area enclosed in a is the greatest
yes
So we are essentially looking for the area there.
@FoolForMath , I give up/
;/
I can give you the answer though, me being a cheater cheater.
what's the answer?
i wish i could do this math. -_-
Give me a second.
I'm going to numerically evaluate the integral with wolfram Mathematica
1.78966
@lgbasallote , here you go.
the answer is wrong
WHAT?
Try the square root of pi then.
as the answer?
Yes.
wrong
btw, try 1.790 if you haven't already.
i did its wrong
Ahem.
;(
lol why call me =)) i only know algebra :P i dont like these stuffs
:((
Wrong, call >.<
http://www.wolframalpha.com/input/?i=integral%5B2+sin%28x%5E2%29%2C%7Bx%2C0%2Csqrt%28pi%29%7D%5D
So, you are supposed to use an estimation method that isn't accurate, nor do I know. Or, the problem is set up funy.
Got any more info about what you are learning right now?
If I used the methods they gave, I might just get the answer they are looking for.
i got the answer is y = 10.16912...
That's th correct answer?
|dw:1334818371099:dw|
yes
so\[\int\limits_{1}^{\sqrt{\pi}}f(x) = F(\sqrt{\pi}) - F(1)\] all you need to do is find approximation for definite integral
Well, then I'm completely useless.
10.170 is the answer
Nice job.
thanks anyways
how old are you?
15
I'm still not sure how I missed that problem so badly. :/
15? really?
http://www.wolframalpha.com/input/?i=integrate+2sin%28x^2%29+dx+from+1+to+sqrt%28pi%29 add 9 to get answer
yes dumbcow
sorry for being redundant, i know you already got the answer just putting it out there for everyones benefit
I believe graph would go like this. (the pitch decreasing with increase in x) |dw:1334819574505:dw|
btw, yes, I'm trying to jump the gun and finish calculus and some math afterwards before I enter college.

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