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Ldaniel
Group Title
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 ≈
 2 years ago
 2 years ago
Ldaniel Group Title
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 ≈
 2 years ago
 2 years ago

This Question is Closed

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
set 2sin(x^2)=0
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Wait, over an interval _
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Ignore the interval, and just solve that trig equation.
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
i know that the answer for part "a" is
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
square or sqrt?
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
i dont know how to do part b
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Well, your interval s defined only up to 3. Is that supposed to be that way, or is the three suposed to be pi?
 2 years ago

RaphaelFilgueiras Group TitleBest ResponseYou've already chosen the best response.0
a)\[2*\sin(2*x)=0\rightarrow x=k*pi/2\] In this interval x=pi/2
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Do you understand a though?
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
well i got x= dw:1334814197335:dw
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
dw:1334814169184:dw
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
and is the right answer
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
dw:1334814236680:dw
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Naturally, sqrt pi would be the largest value up to 3, because it squares out to pi.
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
the equation is f(x) = 2sin(x^2)
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
sorry about that
 2 years ago

RaphaelFilgueiras Group TitleBest ResponseYou've already chosen the best response.0
\[F(x)=\cos(2*x)+K'\] \[F(1)=\cos(2*1)+K'=9\]
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
I know  That is sin x
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
but, sin x^2 is similar to the graph in that it has its highest values at sqrtpi
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
sqrt(pi) is the right answer for part a is marking it right
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
the part that i dont get how to do is part b
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Yes. Can you tell me what calc course you are enrolled in?
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Alright, give me a second.
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
2sin(x^2) = 0 x^2 = pi x = sqrt(pi)
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
thats how i got my answer
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Have you learned how to approximate integrals?
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
thats what we are learning
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
What's it called?
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
antiderivatives
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
No, what kind of approximations have you learned?
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
I just figured out how I can solve the problem.
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Here's the graph, btw
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
i dont know
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
http://www.wolframalpha.com/input/?i=integrate+2+sin%28x%5E2%29
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
the tittle of this chapter is antiderivatives
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
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
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
so how do i do part b?
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
I'm thinking ;)
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Have you learned trapozoidal approximation?
 2 years ago

noginogi Group TitleBest ResponseYou've already chosen the best response.0
I also have a question for part b... help us figure this out plz
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
http://www.wolframalpha.com/input/?i=+2+sin%28x%5E2%29
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Alright. that is the graph of f(x)=2 sin(x^2) right?
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Notice how the waves become wider and wider close to 0.
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
after that, they become thinner and thinner.
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Now, give me a second to explain something.
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Let me get htis plot into mathematica, and show you what I'm talking about.
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Ok. The area of a>b>c>d Tell me if you understand.
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
@Ldaniel ?
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
So, because of this, we know that from 0 to 3, the area enclosed in a is the greatest
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
So we are essentially looking for the area there.
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
@FoolForMath , I give up/
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
I can give you the answer though, me being a cheater cheater.
 2 years ago

noginogi Group TitleBest ResponseYou've already chosen the best response.0
what's the answer?
 2 years ago

mr.luna Group TitleBest ResponseYou've already chosen the best response.0
i wish i could do this math. _
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Give me a second.
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
I'm going to numerically evaluate the integral with wolfram Mathematica
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
@lgbasallote , here you go.
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
the answer is wrong
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Try the square root of pi then.
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
as the answer?
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
btw, try 1.790 if you haven't already.
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
i did its wrong
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
lol why call me =)) i only know algebra :P i dont like these stuffs
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Wrong, call >.<
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
http://www.wolframalpha.com/input/?i=integral%5B2+sin%28x%5E2%29%2C%7Bx%2C0%2Csqrt%28pi%29%7D%5D
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
So, you are supposed to use an estimation method that isn't accurate, nor do I know. Or, the problem is set up funy.
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Got any more info about what you are learning right now?
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
If I used the methods they gave, I might just get the answer they are looking for.
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
i got the answer is y = 10.16912...
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
That's th correct answer?
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
dw:1334818371099:dw
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
so\[\int\limits_{1}^{\sqrt{\pi}}f(x) = F(\sqrt{\pi})  F(1)\] all you need to do is find approximation for definite integral
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
Well, then I'm completely useless.
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
10.170 is the answer
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
thanks anyways
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
how old are you?
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
I'm still not sure how I missed that problem so badly. :/
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
15? really?
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
http://www.wolframalpha.com/input/?i=integrate+2sin%28x^2%29+dx+from+1+to+sqrt%28pi%29 add 9 to get answer
 2 years ago

Ldaniel Group TitleBest ResponseYou've already chosen the best response.1
yes dumbcow
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
sorry for being redundant, i know you already got the answer just putting it out there for everyones benefit
 2 years ago

apoorvk Group TitleBest ResponseYou've already chosen the best response.0
I believe graph would go like this. (the pitch decreasing with increase in x) dw:1334819574505:dw
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.3
btw, yes, I'm trying to jump the gun and finish calculus and some math afterwards before I enter college.
 2 years ago
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