Question

integration problem

Answer 1

\[\int\limits_{}^{}\sin(x^2)dx\]

Answer 2

am I substituting x^2 or the entire function?

Answer 3

well-known non-integrable indefinite form
http://www.wolframalpha.com/input/?i=integral%20sin(x%5E2)dx&t=crmtb01

Answer 4

is this part of a larger problem?

Answer 5

u = x^(2)

du/dx =du/dx x^2
du/dx = 2x
du = 2x dx
du/2x = dx

thus we have the integral

\[\int\limits_{}^{}\frac{\sin(u)du}{2x}\]

Answer 6

yes it is. its a rotation problem

Answer 7

yeah you are right

Answer 8

oo i didn't know I can divide the x in a substitution

Answer 9

this integral is famously not representable in terms of simple functions

...you can't, that's where you get stuck

Answer 10

well you have \[\frac{1}{2}\int\limits_{}^{}\frac{\sin(u)du}{(u)^{1/2}}\]

Answer 11

yeah substitution wont work

Answer 12

then integration by parts goes around in circles, so you have to do some fancy trick

Answer 13

enlighten us turningtest with your fancy trick

Answer 14

ooo i forgot about integration by parts as well

Answer 15

I forget what exactly the deal is, I think it need to be converted in polar coordinates and made into an improper integral
beyond my ability
@mukushla or @experimentX may have an idea

Answer 16

looks like you could relate this to the gamma functions somehow too, but I'm on pretty shaky ground with that stuff

Answer 17

Don't you have use series

Answer 18

I remember reading in my calculus textbook that you need series to solve problems such as these

Answer 19

this is pretty easy .. if you wolfram first ... you know where to go then

Answer 20

wolfram says we need the fresnal integral...

Answer 21

I don't know what that is, so...

Answer 22

probably makes more sense as a definite integral

Answer 23

https://en.wikipedia.org/wiki/Fresnel_integral

Answer 24

this doesn't have closed form in elementary integral ... i guess that's special function.

Answer 25

woo i was correct you do use series to solve this

Answer 26

that's what I said, there is no elementary representation

Answer 27

am i doing the wrong thing by integrating sin(x^2) if the problem is this:
A y = f(x) = sin(x^2) is revolved around the y-axis for x = 0 and x = (pi)^(1/2)

Answer 28

series is one possible representation, but I don't think anything gets "solved" by using series
it's just another way to write the fesnal integral

Answer 29

fresnel*

Answer 30

and I'm asked to find the volume*

Answer 31

what course are you in mbernard91

Answer 32

calc 2

Answer 33

well that x=(pi)^(1/2) part is probably important here if you look at the wiki

Answer 34

crazy we didnt touch anything like this in calc 2

Answer 35

this makes more sense when this is a definite integral ...

Answer 36

indeed^

Answer 37

lol sorry guys

Answer 38

still doesn't make it easy though, not for me at least...

Answer 39

couldn't you just integrate the series and then convert that back to a function

Answer 40

i don't know much about series to be honest.

Answer 41

or would it be too difficult to go from the series to a function

Answer 42

integrated series to a function

Answer 43

using the disk method the integral is\[\int_0^{\sqrt\pi}x\sin(x^2)dx\]so now it's easy u-sub material

Answer 44

sorry I mean shell method

Answer 45

oo okay you're absolutely right

Answer 46

radius=x
height=f(x)

Answer 47

you get the picture :)