(1) Integrate f(x, y,z)+Vy - z2 over the straight line segment path from (0,0,0) to (1,1,1) (2) Consider the field F (2xyz+2,x2z, x2y), (a) (b) (c) Show that the field is conservative. Find a potential function for the field. Find the work the field does on an object that follows the path consisting of the line segment from (0,0,0) to (1,2,2), followed by the line segment from (1,2,2) to (2,4,3) Find the work done by the field ß-(x, 3y,-5z) along...
3. Let (a) Show that F is conservative in R3. (b) Let T denote the triangular path with vertices (1,1,1), (2,1,1) and (3,2,2), traversed from ,1) to (2,1,1) to (3,2,2) to (1,1,1). Evaluate F.dr Justify your answer (c) Find a function p: R3R such that F Vp. (d) Evaluate dr, where Г is the path y-12, z-0, from (0,0,0) to (2,4,0) followed by the line seqment from (2, 4,0 to 1, 1,2)
3. Let (a) Show that F is conservative...
what is the answer?
(1 point) Finding the length of a curve. Arc length for y = f(x). Let f(x) be a smooth function over the interval [a, b]. The arc length of the portion of the graph of f(x) from the point (a, f(a)) to the point (b, f(b)) is given by V1 + [f'(x) dx Part 1. Let f(x) = 2 ln(x) - Setup the integral that will give the arc length of the graph of f(x) over...
Find the arc length parameter along the curve from the point where t=0 by evaluating the integral s | |vIdT. Then find the length of 0 the indicated portion of the curve. The arc length parameter is s(t) (Type an exact answer, using radicals as needed.) Find T, N, and k for the plane curve r(t) (2t+9) i+ (5-t2) j T(t)= (Type exact answers, using radicals as needed.) (Type exact answers, using radicals as needed.)
Find the arc length parameter...
ili Quot 12.3.14 Find the arc length parameter along the curve from the point where t = 0 by evaluating the integral s - Sivce)| dr. Then find the length of the indicated portion of the curve. -jwel de r(t)- (5 + 3)i + (4 +31)j + (2-7)k, - 1sts The arc length parameter is s(t)=0 (Type an exact answer, using radicals as needed.)
(1 point) Consider the vector field F(x, y, z) = (2z + 3y)i + (2z + 3x)j + (2y + 2x)k. a) Find a function f such that F = Vf and f(0,0,0) = 0. f(x, y, z) = b) Suppose C is any curve from (0,0,0) to (1,1,1). Use part a) to compute the line integral / F. dr. (1 point) Verify that F = V and evaluate the line integral of F over the given path: F =...
2. (20 marks) A rose by any other name... () (5 arks) The equation for arc length we have seen in lectures is: dr Convert this to an arc length of a curve that is given in polar coordinates (b) (5 marks) Investigate 'rose curves' and summarise what they are. (c) (5 marks) Determine the integral that should be used to determine the arc length of a rose curve and explain why a solution will not be possible (d) (5...
What is the value of ScF. Tds, where F(x, y, z) = y² i + 2xzj + 6xk and C is the straight-line segment r(t) = ti + tj + tk, 0 <t<1 from (0,0,0) to (1,1,1)?
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.
Find the length of the arc of the curve from point P to point Q. y = {x?, A(-7,4), (7,00)