Q3. Find the value of integral [F.di, where C is the semicircle parameterized by r(t) =...
Question 2 0.3 pts If the curve C is the top semicircle x2 + y2 = 4 from (2,0) to (-2,0), evaluate the line integral / (x + y) ds. (enter an integer or a fraction) Question 3 0.3 pts Calculate the work done by the force field F = (x, -y, z) along the path r(t) = (cost, sint, 2t), osts T TT 4 2 1 0 0 0 0 2 72 1 4 O 72 4
Evaluate the line integral ∫C.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) = t3 i- t3j + tk, 0 ≤ t ≤ 1 .
Evaluate the line integral ∫ F *dr
where C is given by the vector function
r(t).
F(x, y, z) =
(x + y2) i +
xz j + (y + z)
k,
r(t) =
t2i +
t3j − 2t
k, 0 ≤ t ≤ 2
1. Find 12 + y² + 22 ds where is the helix r(t) = (a cost, a sint, bt) and 0 <t<l. 2. Evaluate |(2.84 +248, +16) - dr where C' is a curve that begins at (0,1) and ends at (1,2).
(1 point) Calculate the integral of f(x, y, z)-3x2 + 3уг + z6 over the curve c(t) (cost, sint, t) for 0 < t < π
(1 point) Calculate the integral of f(x, y, z)-3x2 + 3уг + z6 over the curve c(t) (cost, sint, t) for 0
9. Evaluate the “vector valued” line integral 1.Podr Fodr where F(x, y, z) = (x, y, zy) TT and C is given by r(t) = (sint, cost, t), with N » 4. u sta
13. (10 points) (a): Find the line integral of f(x, y, z) = x+y+z over the straight-line segment from (1,2,3) to 0,-1,1). (b): Find the work done by F over the curve in the direction of increasing t, where F=< x2 + y, y2 +1, ze>>, r(t) =< cost, sint,t/27 >, 0<t<27.
(4) Evaluate the line integral F dr where C is the epicycloid with parametrization given by r(t) 5 cos t - gradient of the function f(x, y) = 3 sin(ry) + cos(y2) cos 5t and y(t) = 5 sin t - sin 5t for 0 < t < 2« and F is the (5) EvaluateF dr where F(x, y) with counterclockwise orientation (2y, xy2and C is the ellipse 4r2 9y2 36 _ F dr where F(r, y) = (x2 -...
Write the line integralſ, F. dr as a definite integral of a real-valued function. Do not evaluate. where F(x, y, z)=(-x, yz,x+y) and C is the helix r(t) = (cost, sint,t); 051521.
et F(r, v) (3z2e* + sec z tan z,ze - 90y*). (a) Show that F is a conservative. (b) Find a function f (potential function) show that F Vf. (c) Use above result to evaluate JeFdr, where C is a smooth curve that begin at the point (2, 1) and ends at (0, 3). (cost, sint) from -2 to t = 줄 particle that moves along the curve. (Write the value of work done without evaluating d) Find the work...