Question
Evaluate the line integral
SC F · dr, where C is given by the vector function r(t).
F(x, y, z) = sin x i + cos y j + xz k
r(t) = t^4i − t^3j + tk, 0 ≤ t ≤ 1
SC F · dr, where C is given by the vector function r(t).
F(x, y, z) = sin x i + cos y j + xz k
r(t) = t^4i − t^3j + tk, 0 ≤ t ≤ 1
Answers
Steve
F·dr = sinx dx + cosy dy + xz dz
Now just crank it out, using the definitions of x,y,z:
∫4t^3 sin(t^4) - 3t^2 cos(t^3) + (t^4)(t) dt
= -cos(t^4) - sin(t^3) + 1/6 t^6 [0,1]
= -1 + 1/6
= -5/6
Now just crank it out, using the definitions of x,y,z:
∫4t^3 sin(t^4) - 3t^2 cos(t^3) + (t^4)(t) dt
= -cos(t^4) - sin(t^3) + 1/6 t^6 [0,1]
= -1 + 1/6
= -5/6