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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 ≈
 one year ago
 one year 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 ≈
 one year ago
 one year ago

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inkyvoydBest ResponseYou've already chosen the best response.3
Wait, over an interval _
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
Ignore the interval, and just solve that trig equation.
 one year ago

LdanielBest ResponseYou've already chosen the best response.0
i know that the answer for part "a" is
 one year ago

LdanielBest ResponseYou've already chosen the best response.0
i dont know how to do part b
 one year ago

inkyvoydBest 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?
 one year ago

RaphaelFilgueirasBest 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
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
Do you understand a though?
 one year ago

LdanielBest ResponseYou've already chosen the best response.0
well i got x= dw:1334814197335:dw
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
dw:1334814169184:dw
 one year ago

LdanielBest ResponseYou've already chosen the best response.0
and is the right answer
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
dw:1334814236680:dw
 one year ago

inkyvoydBest 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.
 one year ago

LdanielBest ResponseYou've already chosen the best response.0
the equation is f(x) = 2sin(x^2)
 one year ago

RaphaelFilgueirasBest ResponseYou've already chosen the best response.0
\[F(x)=\cos(2*x)+K'\] \[F(1)=\cos(2*1)+K'=9\]
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
I know  That is sin x
 one year ago

inkyvoydBest 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
 one year ago

LdanielBest ResponseYou've already chosen the best response.0
sqrt(pi) is the right answer for part a is marking it right
 one year ago

LdanielBest ResponseYou've already chosen the best response.0
the part that i dont get how to do is part b
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
Yes. Can you tell me what calc course you are enrolled in?
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
Alright, give me a second.
 one year ago

LdanielBest ResponseYou've already chosen the best response.0
2sin(x^2) = 0 x^2 = pi x = sqrt(pi)
 one year ago

LdanielBest ResponseYou've already chosen the best response.0
thats how i got my answer
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
Have you learned how to approximate integrals?
 one year ago

LdanielBest ResponseYou've already chosen the best response.0
thats what we are learning
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
No, what kind of approximations have you learned?
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
I just figured out how I can solve the problem.
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
Here's the graph, btw
 one year ago

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

LdanielBest ResponseYou've already chosen the best response.0
the tittle of this chapter is antiderivatives
 one year ago

inkyvoydBest 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
 one year ago

LdanielBest ResponseYou've already chosen the best response.0
so how do i do part b?
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
Have you learned trapozoidal approximation?
 one year ago

noginogiBest ResponseYou've already chosen the best response.0
I also have a question for part b... help us figure this out plz
 one year ago

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

inkyvoydBest ResponseYou've already chosen the best response.3
Alright. that is the graph of f(x)=2 sin(x^2) right?
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
Notice how the waves become wider and wider close to 0.
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
after that, they become thinner and thinner.
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
Now, give me a second to explain something.
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
Let me get htis plot into mathematica, and show you what I'm talking about.
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
Ok. The area of a>b>c>d Tell me if you understand.
 one year ago

inkyvoydBest 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
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
So we are essentially looking for the area there.
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
@FoolForMath , I give up/
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
I can give you the answer though, me being a cheater cheater.
 one year ago

mr.lunaBest ResponseYou've already chosen the best response.0
i wish i could do this math. _
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
I'm going to numerically evaluate the integral with wolfram Mathematica
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
@lgbasallote , here you go.
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
Try the square root of pi then.
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
btw, try 1.790 if you haven't already.
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
lol why call me =)) i only know algebra :P i dont like these stuffs
 one year ago

inkyvoydBest 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
 one year ago

inkyvoydBest 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.
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
Got any more info about what you are learning right now?
 one year ago

inkyvoydBest 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.
 one year ago

LdanielBest ResponseYou've already chosen the best response.0
i got the answer is y = 10.16912...
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
That's th correct answer?
 one year ago

dumbcowBest 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
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
Well, then I'm completely useless.
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.3
I'm still not sure how I missed that problem so badly. :/
 one year ago

dumbcowBest 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
 one year ago

dumbcowBest 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
 one year ago

apoorvkBest 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
 one year ago

inkyvoydBest 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.
 one year ago
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