Find the line integral along the curve from the origin along the x-axis to the point...
Evaluate the integral ∮CF⋅dr for F=(5x2y)i+(2x2−5xy2)j on the curve C consisting of the x-axis from x=0 to x=3, the arc of the circle x2+y2=9 up to the line y=x, and the line y=xdown to the origin. ∮CF⋅dr= Evaluate the integral h. F . dr for F = (5x2 y)i + (2x2-5yj on the curve C consisting of the x-axis from x=0 tox-3, the arc of the circle x2 + y2-9 up to the line y=x, and the line y=xdown to...
(1 pt) For the vector field G- y zy + 4 cos 4x + Ууг+ rezy + cos 4x + y) j find the line integral of counterclockwise around the circumterence ot the circle2+y4 to the point (2/2,2// along the curve C om the ongin along the r a s to the point 2.0) and then (1 pt) For the vector field G- y zy + 4 cos 4x + Ууг+ rezy + cos 4x + y) j find the...
No 3 putin uhd e integral lound a r the val- 0 VIIl, 81. EXERCISES Compute the curve integrals of the vector field over the indicated curves. (x,y)=(x2-2xy,y2-2xy) along the, parabola y=x2 from (-2,4) to 2. 0x, y, xz - y) over the line segment from (0,0, 0) to (1, 2, 4), 3, Let r (x2 y2)1/2 Let F(X)-X. Find the integral of F over the circle of radius 2, taken in counterclock wise direction. 4. Let C be a...
RSS3 points 12. Find the point on the curve y=Vx that is a minimum distance from the point (4,0). Report your answer as an ordered pair in the format (x, y) and round each coordinate to the nearest tenth. 13. Consider all lines in the xy-plane that pass through both the origin and a point (x, y) on the graph of the parabola y = x^2 - x + 16 for (1,8). The figure below shows one such line and...
PROBLEM 3 Calculate the line integral of the function from the origin to the point (2,2,2) by three different routs: 1 (0,0,0)- (2,0,0)(2,2.0) (2.2.2) 2. (0, 0,0)-(0,0, 2)(0, 2,2)- (2, 2, 2) 3. the straight line (0, 0,0) (2, 2,2) 4. What is the line integral around the closed loop that goes out along path 1) and returns back along path (2)?
Notation and convention: r x +y The distance from the origin to the point r [x,y,z] + ê: The unit vector along the direction of r-[x, y,z] (a.e,6)-i.j.):m :The orthonormal bases of a Cartesian coordinate system. for dummy indices Einstein convention: Omitting the summation notation (repeated indices). Examples:ab,-a b, ab a b Notice: No dummy index is allowed to be repeated more than twice. You should change the "names" of the dummy indices before taking the product of two summations...
Suppose F⃗(x,y)=(x+6)i⃗+(5y+5)j⃗. Use the fundamental theorem of line integrals to calculate the following (a) The line integral of F⃗→ along the line segment C from the point P=(1,0) to the point Q=(4,2). ∫CF⃗⋅dr⃗∫= (b) The line integral of F⃗→ along the triangle C from the origin to the point P=(1,0) to the point Q=(4,2) and back to the origin. ∫CF⃗⋅dr⃗∫=
Problem 3 (16 2 3 points): Static Magnetic Field: A wire carrying current lo runs from y = to theo along the y-axis and then from the origin to x along the x-axis. Use the Biot- Savart Law to determine the magnetic flux density at the point indicated in the figure. (хо.yo) Problem 3 (16 2 3 points): Static Magnetic Field: A wire carrying current lo runs from y = to theo along the y-axis and then from the origin...
Evaluate the line integral, where C is the given curve. where C is the curve of intersection of the sphere and the plane oriented counterclockwise when viewed from the positive x-axis. We were unable to transcribe this image-- + +22=1 r - y=0
A line of charge with uniform density of 32.0 nC/m lies along the line y = -15.0 cm, between the points with coordinates x = 0 and x = 48.0 cm. Find the electric field it creates at the origin. Magnitude N/C Direction ° (counterclockwise from the +x axis)