Question

x/dx ∫sin(x^2)dx

Answer 1

??

Answer 2

\[{d \over dx} \int\limits_{} \sin^2x dx\]

Answer 3

no \[\sin(x^{2})\]

Answer 4

well the \[d \over dx\] part means "take a derivative with respect to x"

and the \[\int\limits_{} dx\] part means take an antiderivative with respect to x.

Answer 5

what happens when you take the derivative of an anti-derivative?

Answer 6

where do you finf the equation insert for where you ask a question. I keep resorting to using microsoft word and it does not translate well. O, you are left with the function you were taking the integral of

Answer 7

yes sir!

Answer 8

How is this one different
\[d/dx \int\limits_{0}^{x} \sin(t^{2})dt\]

Answer 9

I would just evaluate that one..

Answer 10

do u-sub for t^2

Answer 11

notice how the derivative is with respect to x and the integral is with respect to t...

Answer 12

but the integral is evaluated over x

Answer 13

which means there will probably be an x in the solution

Answer 14

then you can take the derivative of that...

Answer 15

this one ends up as sin (x^2) as well

Answer 16

Thanks, you really cleared up the confusion I was having.

Answer 17

yea no problem.. There is a different way of thinking about this last problem without actually doing the math if you want me to explain it

Answer 18

sure

Answer 19

can you split up the question to look like\[d/dx \int\limits_{}^{}\sin(x ^{2})dx - d/dx \int\limits_{}^{}\sin(0^{2})dx\]

Answer 20

\[{d \over dx} \int\limits_{0}^{x} \sin(t^2) dt \]
thats the same as
\[{d \over dx} \int\limits_{}^{} \sin(x^2) dx - {d \over dx} \int\limits_{}^{} \sin(0^2) dx\]

Answer 21

yea exactly

Answer 22

o ok

Answer 23

but be careful doing that...

Answer 24

I'm not exactly sure when that works and when it doesn't

Answer 25

ok. Yeah I was origonally taking the integral of sin(t^2) then trying to take the derivative.

Answer 26

that will work too

Answer 27

is the integral of sin(t^2)
\[-\cos(t ^{2}) \over 2t\]

Answer 28

hmm actually i think you have to do it the way we did it the second time becuase now that i think about it it seems like thats a pretty tricky integral to do by hand

Answer 29

Ok that sounds good thanks again

Answer 30

np