jennychan12
Find an antiderivative F of f(x) = x^2*sin(x^2) such that F(1) = 0.
Delete
Share
This Question is Closed
jennychan12
Best Response
You've already chosen the best response.
0
I don't think you can use u-sub here. cuz then it'd be f(u) = u*sinu..
jennychan12
Best Response
You've already chosen the best response.
0
and i haven't learned trig sub or integration by parts yet.
Argos
Best Response
You've already chosen the best response.
0
jenny you are a liar i think
jennychan12
Best Response
You've already chosen the best response.
0
-_-
i haven't.
but i can do integration by parts. but my teacher never taught it.
Argos
Best Response
You've already chosen the best response.
0
becos that problem required fresnal integral
jennychan12
Best Response
You've already chosen the best response.
0
what?
wio
Best Response
You've already chosen the best response.
1
Use \(u = x^2\). Then \(x = \sqrt{u}\)
Argos
Best Response
You've already chosen the best response.
0
u can use u sub on that
jennychan12
Best Response
You've already chosen the best response.
0
\[f(x) = x^2\sin(x^2) \]
jennychan12
Best Response
You've already chosen the best response.
0
if u = x^2 then du = 2xdx
Argos
Best Response
You've already chosen the best response.
0
well what method are you allowed to use if you can't use trig or parts
jennychan12
Best Response
You've already chosen the best response.
0
that's what i don't understand.
u-sub doesn't really work...
Argos
Best Response
You've already chosen the best response.
0
so ur on u-sub section of the book?
jennychan12
Best Response
You've already chosen the best response.
0
no it's a review packet. i learned area, u-sub, trapezoid rule, and simpson's rule
igotzbeard
Best Response
You've already chosen the best response.
0
thats the way it is
igotzbeard
Best Response
You've already chosen the best response.
0
not an exponent
jennychan12
Best Response
You've already chosen the best response.
0
no it's
\[f(x) = x^2\sin(x^2)\]
wio
Best Response
You've already chosen the best response.
1
This isn't a candidate for u sub.
igotzbeard
Best Response
You've already chosen the best response.
0
u = x^2
du = 2x dx cant use u du sub
igotzbeard
Best Response
You've already chosen the best response.
0
no place to apply a substitution
wio
Best Response
You've already chosen the best response.
1
\[
\frac{1}{2}\int \sqrt{u}\sin(u)du
\]Isn't helpful.
k.rajabhishek
Best Response
You've already chosen the best response.
0
|dw:1357267172296:dw|
jennychan12
Best Response
You'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
Best Response
You've already chosen the best response.
2
whats the name of the textbook
jennychan12
Best Response
You've already chosen the best response.
0
although i know how to do parts but my teacher never taught it.
jennychan12
Best Response
You've already chosen the best response.
0
stewart
LogicalApple
Best Response
You've already chosen the best response.
2
7th edition?
jennychan12
Best Response
You've already chosen the best response.
0
5th
LogicalApple
Best Response
You've already chosen the best response.
2
which chapter section?
jennychan12
Best Response
You've already chosen the best response.
0
chapter 5 review #49
Argos
Best Response
You've already chosen the best response.
0
integral 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
Best Response
You've already chosen the best response.
0
fresnal function is introduced in section 5.3
igotzbeard
Best Response
You've already chosen the best response.
0
lol wolframalpha? xD
jennychan12
Best Response
You've already chosen the best response.
0
haha same
5.3 is fundemental theorum
Argos
Best Response
You've already chosen the best response.
0
go to 5.3 examlpe number 3
jennychan12
Best Response
You've already chosen the best response.
0
we don't use stewart. we use larson. my teacher just photocopied this from the stewart textbook
Argos
Best Response
You've already chosen the best response.
0
thats illegail
Argos
Best Response
You've already chosen the best response.
0
but u gonna have to look up fresnal function elsewhere then
jennychan12
Best Response
You've already chosen the best response.
0
she owns like ten stewart textbooks.
-_-
i'll just use parts then...
LogicalApple
Best Response
You've already chosen the best response.
2
I 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
Best Response
You've already chosen the best response.
2
wait let me rewrite that
LogicalApple
Best Response
You've already chosen the best response.
2
\[F(x) = \int\limits\limits_{1}^{x} t ^{2} \sin(t ^{2}) dt\]
LogicalApple
Best Response
You've already chosen the best response.
2
That way when it is evaluated at F(1), you still get 0. And the derivative is the original function.
wio
Best Response
You've already chosen the best response.
1
If you used Simpson's rule or Midpoint rule on that, you'd get a nasty summation but it is within the rules.
jennychan12
Best Response
You've already chosen the best response.
0
oh wow. thanks @LogicalApple
that's the answer in the book
-___-
LogicalApple
Best Response
You've already chosen the best response.
2
Well 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
Best Response
You've already chosen the best response.
0
yes but i never thought of it that way...
*sigh*
LogicalApple
Best Response
You've already chosen the best response.
2
Stewart doesn't mess around.. I'm in chapter 5 on the 7th edition.
jennychan12
Best Response
You've already chosen the best response.
0
oh same here i think.
my teacher uses both stewart and larson. we teach from larson.
LogicalApple
Best Response
You've already chosen the best response.
2
I will have to check that one out. Anyway good luck with your studies!
jennychan12
Best Response
You've already chosen the best response.
0
thanks :)
wio
Best Response
You've already chosen the best response.
1
I think it's sort of an unfair question. Should have specified a bit more the rigor.
jennychan12
Best Response
You've already chosen the best response.
0
same. my teacher likes stewart because they have "more pictures" and "good problems". which means that she puts them on quizzes and tests. :[
jennychan12
Best Response
You've already chosen the best response.
0
i guess it just makes u think about the concept more?
wio
Best Response
You've already chosen the best response.
1
If they said something like "in terms of an indefinite integral" then it would have been fair.
LogicalApple
Best Response
You've already chosen the best response.
2
Yeah sometimes Stewart's questions are very very chapter-specific That's why I asked what chapter the problem was in to get an idea of the context of the question.