Line Integral: Evaluating Along Circular Path from P1 to P2

Cryphonus
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Homework Statement



Evaluate the line integral along the segment P1(0,3) to P2(-3,0) of the circular path shown in figure.

Figure basically shows a circle with a radius of 3. The part that i have to evaluate is from the y-axis (P1) to the x-axis (P2), basically a quarter of the circle.



Homework Equations



integral from P1 to P2 of E.dl



The Attempt at a Solution



I just can't write the equation to begin with.

i would be glad if you can give me some hints about the equation that i have to integrate, thanks a lot!
 
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Cryphonus said:

Homework Statement



Evaluate the line integral along the segment P1(0,3) to P2(-3,0) of the circular path shown in figure.

Figure basically shows a circle with a radius of 3. The part that i have to evaluate is from the y-axis (P1) to the x-axis (P2), basically a quarter of the circle.



Homework Equations



integral from P1 to P2 of E.dl



The Attempt at a Solution



I just can't write the equation to begin with.

i would be glad if you can give me some hints about the equation that i have to integrate, thanks a lot!

I'm afraid there aren't any mind readers here. If you can't write down the equation you need help with, how are we to help you figure out how to work it?
 
oh sorry i thought it was there E= (x) x - (y) y variables in the paranthesis refers to the direction. i still need to express dl somehow.
 
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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