how I can complete the integration? (line integral of vector)

 

Well your next step should be to create two integrals.

Have you done this

Then it looks like a gamma function transformation integral to me, although there are (as always) other ways.

What methods have you been taught for trig functions?

edit presumably there should be a 'dt' in there somewhere?

 

and write this properly... where is dt?

 

Can you integrate

\(
\int{u dt}
\)

or

\(
\int{u^2 dt}
\)

If so, then you are done since those are the forms you have. You just need to substitute 'u' for something in order to make it apparent.

Note that I'm just looking at your last line. Your handwriting is too sloppy for me to be sure that I can make out your earlier stuff.

 

yes, dt

 

yes, dt

??????

 

hello again
how can do integral same wolfram ?

 

Can you integrate

\(
\int{u dt}
\)

or

\(
\int{u^2 dt}
\)

If so, then you are done since those are the forms you have. You just need to substitute 'u' for something in order to make it apparent.

Note that I'm just looking at your last line. Your handwriting is too sloppy for me to be sure that I can make out your earlier stuff.

respect your phrasing

 

I can't see how you get from line 1 to line 2 in your original post.

There should be six terms in line2, not two terms.

So before you go of down some substitution route get the leadup correct.

 

respect your phrasing

What makes you think I don't have respect for my phrasing?

But let's try this: Your otherwise perfect penpersonship has been corrupted, through no fault of your own of course, by the pen, the paper, the camera, and the internet so as to make it less than optimally readable to us inferior beings.

 

I can't see how you get from line 1 to line 2 in your original post.

There should be six terms in line2, not two terms.

So before you go of down some substitution route get the leadup correct.

Could you post what you think his first line is? I can't make a good portion of it. I'm guessing the TS will be offended if I ask him to present his work more clearly.

Like you, I don't see how the first line leads to the second, but I can't make all of that out clearly, either. It would also appear that there's a sign error in going from the second to the third, assuming that that's a plus sign between the two terms on the second line.

 

Best I can do


\(\int\limits_0^{2\pi } {\left( {72\cos t\sin t - 72\sin t + 41} \right)} \bullet \left( { - 2\sin t + 2\cos t} \right)dt\)

edit corrected first bracket

 

Best I can do


\(\int\limits_0^{2\pi } {\left( {72(\cos t\sin t - 72\sin t + 41)} \right)} \bullet \left( { - 2\sin t + 2\cos t} \right)dt\)

That helps. I would have never guessed that was a '41' due to what is just to the right of the '1'. I couldn't tell if that was a 'k', perhaps? It also looks like there is an 'i'-hat unit vector on the first term and maybe on the second term. Or maybe that's a 'j'-hat. Oh, wait a minute, my guess is that this is

\(\int\limits_0^{2\pi } \left[ {72\cos(t)\sin(t) \hat{i} - 72\sin(t) \hat{j} + 4 \hat{k}} \right] \cdot \left[ - 2\sin(t) + 2\cos(t) \right] dt
\)

If so, the TS is making a total hash of things.

So now I'm guessing that what looks like "1uH" or perhaps "1HH" on the second and third lines is actually supposed to be "144".

 

yes I thought that 2x72=144.

but you have probably hit on the meaning of the other squiggles as i,j,k