Use the transformation u = y – r and v = y to evaluate the integral // 2 + s°) dz dy where R is bounded by the lines y =1 y =r+a y = a y = 2a (a > 0).

Q: Find the line integral of F(x, y) = (x²– y², 2.xy) = (P, Q) along the boundary of the rectangle [0,…

A:

Q: Compute the line integral of the scalar function f(x, y) = /1+9xy over the curve y = x³ for 0 < x <…

A:

Q: Compute the line integral of the scalar function f(z,y, 2) = 2z² + 8z over the curve c(t) = (e*, t²,…

A:

Q: Evaluate the line integral I of the one-form w = (y+ z) dx + (x + z) dy + 10z dz over the line…

A: We have to find the line integral.

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 s t s 1. (y - x) dx +…

A:

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 s ts 1. %3D (y – x) dx…

A:

Q: Calculate the integral f, (3y – 3x²) dæ + (9x) dy where y= aD is the counter-clockwise boundary of…

A: we are allow to solve one question at a time thank you

Q: Use Green's Theorem to find the line integral. C is to be traversed in the counterclockwise…

A: In the question it is asked to calculate integral using Green's Theorem.

Q: Evaluate the line integral by applying Green's theorem. 7xy dx + (x + y) dy, where C is the boundary…

A:

Q: Calculate the integral of f(x, y, z) = 3x² + 3y² + zª over the curve c(t) = (cos t, sin t, t) for 0…

A:

Q: Evaluate the line integral Lav where C is given by the line y = lnx, 1 ≤ x ≤e. xy ds,

A:

Q: 'ind the line integral of F(x, y) = (x² – y² , 2xy) = (P, Q) along the boundary of the rectangle %3D…

A:

Q: Calculate the line integral [(of).do where f(x, y, z) = x ² ¹² + 4 xy² z yz с + е хуча and C is the…

A:

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [ (v - x) dx +…

A:

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

A:

Q: Suppose that f(z, y) = /4 – a² – y² at which {(r, y) | 2² + y² < 4}. Then the double integral of…

A:

Q: + y^5)dy] where C is the unit circle x^2 + y^2 = 1 traversed counterclockwise.

A: we have to compute the given integral ∮x5+y3dx-(x3+y5)dy     where C is unit circle x2+y2=1.C

Q: Evaluate the triple integral (x + 2y) dV where E is bounded by the parabolic cylinder y = 7x² and…

A:

Q: Evaluate the following line integral by two methods: (a) directly; (b) using Green's Theorem. $y²dx…

A:

Q: Calculate the value of the line integral fds where f(x, y, z)=e² and C is described by X C (x, y,…

A: The objective of the question is evaluate the definite integral.

Q: Set up an integral for the length of y = vx + 2, 2 2 <x<7 using ds = 1+ ) dy. A. ds = f, /1+ 4y²dy…

A:

Q: Evaluate the line integral S, y ds where C:x = t²,y= 2t, 0 <t < 3

A:

Q: Evaluate the line integral ,F. dr where F = (sin x, –2 cos y, 5xz) and C is the path given %3D by…

A: Integral F.dr = integral F(r(t)).r'(t) dt

Q: Evaluate the line integral ex dx - xy dy +y dz, where c(t) = (1, t, t ), 0 sts 1. %3D

A: As per our guideline we are supposed to answer only first asked question.Kindly repost other…

Q: (a) (x2 + y?) dx dy J2

A: To calculate the integral: ∫-11∫24x2+y2dx dy Solution: When we will integrate with respect to one…

Q: Compute the line integral of the scalar function f(x, y) = /1+ 9ry over the curve y = x° for 0 <¤ <…

A:

Q: 1) := 6z- 4y. D:y=2r. y=1-3 2) = cosr. D:y-2r. p=r,r=T

A:

Q: Let w = e" dx + 4x dy + sin(x1³) dz be a one-form on R³. Find the line integral of w going…

A:

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 s ts 1. (y – x) dx +…

A:

Q: Evaluate the given integral by using a transformation to cylindrical coordinates: f (x2+2)¹/2 dv,…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let 0 < c < 1. Compute the integral rc+ioo dz Jc-ioo sin nz' where the integration path is the…

A: We will use the basic knowledge of complex line integrals to answer this question properly, in…

Q: Evaluate the triple integral ∭E (x+7y)dV where E is bounded by the parabolic cylinder y=2x^2 and the…

A:

Q: Evaluate the line integral x° + y) ds C Where C is given by r(t) = 3ti+t°j for 0<t<1

A: The region C is given by: r(t)=3t i + t3 j  ;       for  0≤t≤1

Q: Compute the line integral of the scalar function f(x,y,z)=2x^2+8zf(x,y,z)=2x2+8z over the curve…

A:

Q: Compute the line integral of the scalar function f(x,y,z)=2x2 +8z over the curve…

A:

Q: Evaluate the line integral Sa y dx +z dy, where C is the line segment from (4) (-1, 1, 2) to (2,3,…

A:

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

A:

Q: Calculate the line integral of h (x, y) = (2xy) i + (x– 2ry) j; over r (u) = cos u i+ sin u j, u E…

A: Given function is  hx,y=2xyi+x2−2xyj To compute the line integral over ru=cosui+sinuj from 0 to 2?.

Q: Evaluate the line integral In(x + y) ds, z + 2 where C is the line segment from the point (1,0, –1)…

A:

Q: Find the line integral along the given path C. Ju- |(x- y)dx, where C: x = t, y = 5t + 6, for 0 sts2…

A:

Q: Evaluate the line integral f F · dr, where F(x, y, z) = –2xi + 3yj + 3zk and C is given by the vecte…

A:

Q: Evaluate the line integral. y dx + z dy + x dz, r(t) = (2 + t-1, t3, t2) for 0 <t< 3

A: Here, x=2+t-1 y=t3 z=t2

Q: Evaluate the line integral INTEGRAL C (x − y 2 )ds where C is given by r(t) = (t^2 + 1)i + (t +…

A:

Q: Calculate the line integral of h (x, y)= (2ŋ) i +(x - 2y)j. over r (u) = cos ui+ sin u j, u €…

A:

Q: Use the Fundamental Theorem of Line Integrals to find the exact value of the path-independent line…

A: First of all hare we check for the path independent line integral then solve for moving over the…

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

A:

Q: Evaluate the triple integral (x + 8y) dV where E is bounded by the parabolic cylinder y = 4x² and…

A:

Q: Evaluate the line integral F dr, where C is given by r(t) = (t², t, vT), 0<ts2 and (x, y, z) = (z,…

A:

Q: A. Evaluate and sketch the line integral :1 = f yx dx + (2X – Y)dy around the region bounded by…

A: Greens theorem

Q: Evaluate the triple integral (x + 8y) dV where E is bounded by the parabolic cylinder y = 4x² and…

A: