Evaluate the line integral(adsbygoogle = window.adsbygoogle || []).push({});

Force field is the integral in the form of integrand ( (2x dx+ 2y dy + 2 zdz)/r^2).

the domain of integral is C,

C = C1 + C2. C1 is the line segment from (1; 2; 5) to (2; 3; 3). C2,arc

of the circle with radius 2 and centre (2; 3; 1) in the plane x = 2. The arc has initial point

(2; 3; 3) and terminal point (2; 1; 1). The abbreviationsr= <x,y,z> and |r| = r

3. The attempt at a solution

I tried the integral with curve one, since the curve one from (1; 2; 5) to (2; 3; 3) is a line segment the function of the following curve I computed with the equation of line r(t)= (1-t)ro + t(r1) where 0<= t <= 1

ro is (1; 2; 5),

r1 is (2; 3; 3),

i was able to find the r (t) and then took the line integral using the force field above,

Now, I have a problem with the C2 which happens to be an arc, i do know that i can parametrize this C2 with respect to t by saying r(t) = <a cost + x0, a sin t + yo, z0>

but not sure how to get the domain t as i am unable to draw this arc by hand. I would really appreciate if some one tell me how to find out the domain of t in C2 or how to draw it

Sorry for the long post,

Thanks in advance,

regards

daku

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# Line integral, vector calculus

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