.... . S Sinx dA where Ris the trangle in xy-plane bounded by the x-anisey the liney=x+and Ehe linex=

Q: Prove that fe, r*dx + rydy = 0 where Co is the line segments from (0, 1) to (0,0) by using…

A:

Q: Evaluate the line integral fo(y+z) ds along the curve C defined by the straight-line segment 2 0, y…

A:

Q: aluate the line integral, where C is the given curve. z2 dx + x2 dy + y2 dz, C is the line segment…

A: Solve integral by changing in terms of t

Q: Evaluate the line integral, where C is the given curve. xyeVZ dy, C: x = 4t, y = 3t2, z = 4t³, 0sts…

A:

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. O x2y dx,…

A:

Q: Find the area bounded by the parametric curve x=t−(1/t), y=t+(1\t) and the line y=2.5.

A:

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 3y3 dx…

A:

Q: Use Green's Theorem to calculate line integral o sin(x²) dx + (3x – y) dy where C is a right…

A:

Q: If f=2yzj -zj+xk,evaluate line integral Fxdr along the curve x=cost,y=sint,z=2cost from t=0 to…

A:

Q: Use a scalar line integral to find the length of the curve r(t) = (20 sin , 20 cos ,5), for 0 < t <…

A: Given

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 4y dx -…

A:

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve 5y³ dx -…

A: We know that , Green's theorem ,  Consider C be a positively oriented  , simple , closed , piecewise…

Q: Calculate the area under y = x2 over [0, 1] using Eq. (11) with the parametrizations (t3, t6) and…

A:

Q: Evaluate the line integral Fdr where F = 4.xyi – 8yj+ 3k and C is a curve given by y = 2x, z = 3…

A: Answer

Q: Use Green's theorem in order to compute the line integral (2sin z + 3y²) dx + (sin(4®) + 2x³) dy…

A:

Q: Evaluate the line integral F. dr, vhere F(z, y) = -yi-rj and C is the curve y = v4-a from (2,0) to…

A: We have to find the line integral

Q: Which of the following integrals represents the length of the parametric curve z = 1+e, y=ť, 3 <t<…

A: In order to know the length of the given parametric curve we will use the formula  where  -----

Q: Show Z=arctan(y/x) satisfies Zxx+Zyy=0.

A:

Q: Evaluate the following line integral along the curve C. - y)ds; C is the line segment r(t) = (t, 3t…

A:

Q: Evaluate the line integral Jo 9x²yzds with respect to s along the с 2 curve C: x=t, y = t², z = /t³…

A:

Q: Sketch the regions enclosed by the given curves. y = 4 cos(7x), y = 4 sin(14x), x = 0, x = T/14 y y…

A:

Q: Evaluate the line integral 2xyz dx + x²z dy + x?y dz where C is an oriented simple curve connecting…

A: Given line integral is,

Q: Compute 6xy da dy, where D is bounded by the curves y = 4 – x2 and y = 2x + 4.

A:

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 6y3…

A: given circle x2+y2=4

Q: (a) Calculate the line integral (4x+2y²)dy where C' is the curve y = 2³, starting from z = 0, y = 0,…

A:

Q: Find the derivative of g in the direction of a = 2i+ curl w at point (0 where น u+2 8 = In- J u =…

A: Given: the function g=lnuu+2, u=z(xy+z2)2, w=cosxyzi+xeyz+1j+xyzk To find: the directional…

Q: Evaluate the line integral Jxy + z)ds where c the arc of circle x + y = 4, z= 0 from (2, 0, 0) to…

A:

Q: Use Green's Theorem to evaluate / F · dĩ, where F = (VE + 3y, 2x + vũ) C consists of the arc of the…

A:

Q: Evaluate the line integral f. y³ dx – x³dy, where C is the positively oriented circle of radius 2…

A:

Q: Compute the integral |(5y + pz2020, ) dx + (19x – e-4ycos(v) sin y) dy over the portion of the…

A:

Q: Evaluate the line integral Sp(xi+ yyj) · dr where D is the oriented curve shown below. (1,1) y = x²…

A:

Q: Evaluate the line integral (y + z) ds along the curve C defined by the straight-line segment æ = 0,…

A:

Q: Use Green's theorem to evaluate the line Integral for the curve C given in the figure. [2y dx + x…

A:

Q: 2. Compute the scalar line integral xy ds where C is the part of the circle of radius 2, centered at…

A: Put x=2cost , y=2sint

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 8y dx…

A: Introduction: Green's theorem is one of calculus' four fundamental theorems, all of which are…

Q: y = sec 0 tan 0 →0 TT 4 4 -Vz

A: We have given a diagram;

Q: Evaluate the line integral S. xyevz dy, C:x = t,y = t²,z = t³,0 < t s 1.

A:

Q: Evaluate the line integral ſp(xi + Vyi) · dr where D is the oriented curve shown below. (1,1) y = x2…

A: We know that r=xi+yj As, the path followed is y=x2 So, r=xi+x2j Let x=t, then  r=ti+t2jdrdt=i+2tj…

Q: Evaluate the line integral 2xyz dx + x²z dy + x?y dz where C is an oriented simple curve connecting…

A:

Q: Evaluate the line integral. e ds where C is the curve given by x=2t, y=3t, 0<t<2

A:

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 2y3 dx…

A:

Q: Find the area bounded by the parametric curve x=cos(t),y=et,0≤t≤π/2, and the lines y=1 and x=0.…

A: Given: x=cost,y=et, 0≤t≤π2

Q: (2x + y)dx + (x + 2y)dy

A: Given integral is:  where C is any curve that joins the point (1,1) with the (2,2).

Q: A) if F=2yi-zj+xk evaluate line integral Fxdr along the curve x=cost,y=sint,z=2cost from t=0 to…

A: Given x = costy = sintz = 2cost As F = 2yi-zj+xk Then F(x,y,z) = 2y , -z , x Thus F(x(t) , y(t) ,…

Q: Find the area bounded by the line y=4 and the curve described parametrically by: x(t) =…

A: Given: y=4x(t)=t-1t,    y(t)=3t+1tSince y=4,  y(t)=3t+1t ⇒ 3t+1t=4⇒3t2-4t+1=0⇒3t2-3t-t+1=0…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 2y3 dx…

A:

Q: Compute the integral 10x/1+ 4y?ds over the curve C: R(t) = (t + 5, t), 0<t< 1.

A:

Q: 2) Use a change of variables to evaluate , zdV; where Dis bounded by the paraboloid z = 16 – x - 4y?…

A: