Line integral and parametrization

Tony11235
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I know this is dumb question but for some reason I have not been able to get the right answer to the following problem:

\int_{c} 2xyzdx+x^2 zdy+x^2 ydz

where C is a curve connecting (1, 1, 1) to (1, 2, 4).

My parametrization is (1, 1+t, 1+3t). My limits are the problem...I think. By the way the correct in answer in the book is 7.
 
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Tony11235 said:
I know this is dumb question but for some reason I have not been able to get the right answer to the following problem:

\int_{c} 2xyzdx+x^2 zdy+x^2 ydz

where C is a curve connecting (1, 1, 1) to (1, 2, 4).

My parametrization is (1, 1+t, 1+3t). My limits are the problem...I think. By the way the correct in answer in the book is 7.

Your parametrization is fine. You said your limits are the problem, but which are you using? Which value t would give your first point? The second?

Alex
 
OMG...I am retarted. :bugeye:
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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