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 2 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 ≈
 2 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 ≈

This Question is Closed

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Ldaniel
 2 years ago
Best ResponseYou've already chosen the best response.12sin(x^2) = 0 x^2 = pi x = sqrt(pi)

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

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

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

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

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

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

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

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.3Note 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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