2) Compute the integral of f along the path c in each of the following cases: (a

Question

2) Compute the integral of f along the path c in each of the following cases:

(a)f(x,y,z) =x +y +yz;c(t) =(sint, cost,t), 0 %u2264t %u22642%u03C0

(b)f(x,y,z) =x +cos^2z;c(t) =(sint, cost,t), 0 %u2264t %u22642%u03C0

(b)f(x,y,z) =x^2;S is the part of the plane x =z inside the cylinder x^2 +y^2 =1

(c)f(x,y,z) =x;S is the part of the cylinder x^2 +y^2 =2xwith 0 %u2264z %u2264 %u221A x^2 +y^2

4 )If F(x) is orthogonal to c%u2019(t) at each point on the curve x=c(t), what can you say about %u222Bc F dot ds?

6) A ring in the shape of the curve x^2 + y^2 = a^2 is formed of thin wire weighing |x| + |y| grams per unit length at (x,y). Find the mass of the ring.

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