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jennychan12
 2 years ago
Find an antiderivative F of f(x) = x^2*sin(x^2) such that F(1) = 0.
jennychan12
 2 years ago
Find an antiderivative F of f(x) = x^2*sin(x^2) such that F(1) = 0.

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jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0I don't think you can use usub here. cuz then it'd be f(u) = u*sinu..

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0and i haven't learned trig sub or integration by parts yet.

Argos
 2 years ago
Best ResponseYou've already chosen the best response.0jenny you are a liar i think

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0_ i haven't. but i can do integration by parts. but my teacher never taught it.

Argos
 2 years ago
Best ResponseYou've already chosen the best response.0becos that problem required fresnal integral

wio
 2 years ago
Best ResponseYou've already chosen the best response.1Use \(u = x^2\). Then \(x = \sqrt{u}\)

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0\[f(x) = x^2\sin(x^2) \]

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0if u = x^2 then du = 2xdx

Argos
 2 years ago
Best ResponseYou've already chosen the best response.0well what method are you allowed to use if you can't use trig or parts

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0that's what i don't understand. usub doesn't really work...

Argos
 2 years ago
Best ResponseYou've already chosen the best response.0so ur on usub section of the book?

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0no it's a review packet. i learned area, usub, trapezoid rule, and simpson's rule

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0no it's \[f(x) = x^2\sin(x^2)\]

wio
 2 years ago
Best ResponseYou've already chosen the best response.1This isn't a candidate for u sub.

igotzbeard
 2 years ago
Best ResponseYou've already chosen the best response.0u = x^2 du = 2x dx cant use u du sub

igotzbeard
 2 years ago
Best ResponseYou've already chosen the best response.0no place to apply a substitution

wio
 2 years ago
Best ResponseYou've already chosen the best response.1\[ \frac{1}{2}\int \sqrt{u}\sin(u)du \]Isn't helpful.

k.rajabhishek
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1357267172296:dw

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0_ it was in the textbook in the chapter 5. we don't do trig sub/parts until chapter 8...

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2whats the name of the textbook

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0although i know how to do parts but my teacher never taught it.

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2which chapter section?

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0chapter 5 review #49

Argos
 2 years ago
Best ResponseYou've already chosen the best response.0integral x^2 sin(x^2) dx = 1/4 (sqrt(2 pi) C(sqrt(2/pi) x)2 x cos(x^2))+constant C(x) is the fresnal C integral Medal pls

Argos
 2 years ago
Best ResponseYou've already chosen the best response.0fresnal function is introduced in section 5.3

igotzbeard
 2 years ago
Best ResponseYou've already chosen the best response.0lol wolframalpha? xD

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0haha same 5.3 is fundemental theorum

Argos
 2 years ago
Best ResponseYou've already chosen the best response.0go to 5.3 examlpe number 3

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0we don't use stewart. we use larson. my teacher just photocopied this from the stewart textbook

Argos
 2 years ago
Best ResponseYou've already chosen the best response.0but u gonna have to look up fresnal function elsewhere then

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0she owns like ten stewart textbooks. _ i'll just use parts then...

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2I guess one way to approach it is: \[F(t) = \int\limits_{1}^{x} t ^{2} \sin(t ^{2})\] This way the integral evaluated at x = 1 results in 0, and its derivative is just the original function

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2wait let me rewrite that

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2\[F(x) = \int\limits\limits_{1}^{x} t ^{2} \sin(t ^{2}) dt\]

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2That way when it is evaluated at F(1), you still get 0. And the derivative is the original function.

wio
 2 years ago
Best ResponseYou've already chosen the best response.1If you used Simpson's rule or Midpoint rule on that, you'd get a nasty summation but it is within the rules.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0oh wow. thanks @LogicalApple that's the answer in the book ___

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2Well it makes sense, right? We don't actually have to take an integration. We know from the fundamental theorem of calculus (either part 1 or 2, i forget) that the derivative of F(x) here is just the inside of the integral evaluated at x. And for the limits of integration, we know that if we integrate from a to a we always get 0. So let a = 1, that way F(1) is an integral evaluated from 1 to 1.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0yes but i never thought of it that way... *sigh*

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2Stewart doesn't mess around.. I'm in chapter 5 on the 7th edition.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0oh same here i think. my teacher uses both stewart and larson. we teach from larson.

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2I will have to check that one out. Anyway good luck with your studies!

wio
 2 years ago
Best ResponseYou've already chosen the best response.1I think it's sort of an unfair question. Should have specified a bit more the rigor.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0same. my teacher likes stewart because they have "more pictures" and "good problems". which means that she puts them on quizzes and tests. :[

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0i guess it just makes u think about the concept more?

wio
 2 years ago
Best ResponseYou've already chosen the best response.1If they said something like "in terms of an indefinite integral" then it would have been fair.

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2Yeah sometimes Stewart's questions are very very chapterspecific That's why I asked what chapter the problem was in to get an idea of the context of the question.
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