Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0), (2,2) and (2,4). a. Directly (using ordinary integral

Q: Evaluate the iterated integral. LLL- 2 x³ y2 + z?dxdydz 0.

A:

Q: Evaluate the iterated integral. 4z (In(x) xe- dy dx dz J3

A: Formulae used∫e-ydy = -e-y + C∫x2dx    = x33 + C ---------------------------------------- I…

Q: Verify Green's Theorem by evaluating both integrals Lv² dx + x² dy dA ax ay for the given path. C:…

A:

Q: Evaluate the line integral by the two following methods. fwox xy dx + x²y3 dy C is counterclockwise…

A: Since, we have to evaluate the line integral given by:-I=∮C xy dx + x2y3  dy -(i)Our aim is to solve…

Q: Compute the double integral of (x – 2y) Væ + 2y o i over the quadrilateral with vertices (0, 0), (4,…

A:

Q: Find the line integral of x ds over C where c is the line segment from (1,0) to (0,1) using two…

A:

Q: Evaluate the line integral along the given path: 1. So ry ds, where C : r(t) = 4ti + 3t²j, 0 < t <…

A:

Q: Evaluate the line integral Ĥ. dř where Ĥ = e" î + [xe" + In(2)] ĵ + º Â and the curve C is defined…

A: Given problem:-

Q: Evaluate the double integral / (a (x² ,2 + 8y) dA, where D is bounded by y = x, y = x°, and x > 0.

A:

Q: Verify Green's Theorem by evaluating both integrals ON aM | y? dx + -x² dy dA ax ay for the given…

A:

Q: Calculate the iterated integral a) [ [ (6xy² – 2x) dy dæ

A: In this question we have to find Double Integration. First find in terms of y and then in terms of…

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where o sts 1. (y – x) dx +…

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Verify Green's Theorem by evaluating both integrals aN | y? dx + x2 dy = dA ax ду for the given…

A: Gshhsg

Q: Verify Green's Theorem by evaluating both integrals ƏN [ 1² dx + 2² dy - [ ] (™N - OM) a dA ax ду…

A:

Q: Evaluate the double integral of f(x, y) = Vx2 + y2 over the triangular region with vertices (0, 0),…

A: We will find out the required double integral.

Q: 4: Use Green's Theorem to evaluate the following integral e dx + (5x+ 6) dy Where C is the triangle…

A: Using green theorem to evaluate the following integral.

Q: 7. Evaluate the line integral by using Green's Theorem feve'dx +2e*dy C is the rectangle with…

A: Green's Theorem, ∫CPdx+Qdy=∬D∂Q∂x-∂P∂ydA Compare ∫CPdx+Qdy=∫Cyexdx+2exdy Implies that, P=yex, Q =…

Q: Verify Green's Theorem by evaluating both integrals y dx + x2 dy = JR dA dy for the given path. C:…

A:

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve.  xy2…

A: Our Aim is to evaluate the line integral along the given positively oriented curve xy2 dx+3x2y dy…

Q: 1. Evaluate the line integral of E-xa, -y a, along the segment P; to P; of the circular path as…

A:

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

A:

Q: Verify Green's Theorem by evaluating both integrals ax dA ду for the given path. C: rectangle with…

A: From: (0, 0) to (5, 0)y=0, dy=0∫ y2 dx+ x2 dy =0From: (5,0) to (5, 9)x=5, dx=0∫09 x2 dy= ∫0925…

Q: Evaluate the iterated integral. V1- x8 dy dx

A: We have to find

Q: Verify Green's Theorem by evaluating both integrals y? dx + x² dy Ne dA ду ax for the given path. C:…

A:

Q: Verify Green's Theorem by evaluating both integrals Lr dx + x* dy = / dA ду x² dy ax for the given…

A: In this question we verify Green's Theorem                 i.e, verify integral  ∫C y2 dx +x2 dy =…

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: Evaluate the iterated integral. V1- x4 dy dx

A: The given integration,           ∫01∫0x31-x4 dy dx

Q: Consider the following line integral. xy dx + x²y dy, Cis counterclockwise around the triangle with…

A:

Q: Verify Green's Theorem by evaluating both integrals aN dA Lv? dx + x² dy = ду ax for the given path.…

A:

Q: Evaluate the line integral by the two following methods. dx + x2 Cis counterclockwise around the…

A:

Q: Use Green's Theorem to evaluate the line integral of C to the function (y − x) dx + (2x − y) dy  for…

A: To evaluate: ∫Cy-xdx+2x-ydy using Green's theorem where C is the boundary of the region lying…

Q: Use Green's Theorem to evaluate the following line integral. Of dy -g dx, where (fg) = (7x2,8y?) and…

A:

Q: Evaluate the line integral below over the path c(t) = (t², sin(#), e-3t+4) over the interval 0 < t <…

A: We have to evaluate the line integral.

Q: Set up a double integral to find the z = x? + y? %3! %3D z = 0

A: We are asked  to set up double integral to find the volume.

Q: Verify Green's Theorem by evaluating both integrals dA [_v² dx + x² dy = [ ] (ON-OM) DA ду for the…

A:

Q: Verify Green's Theorem by evaluating both integrals ON √ y² dx + x² ov - [/(2x - 2M) da dA R ax ду…

A:

Q: 15. Evaluate the line integral J.(3xy* - 6xy ]dx + (4x°y³ - 3x?) dy, where C is any path from (1,2)…

A:

Q: Evaluate the double integral ∬D (x2+2y)dA , where D is bounded by y=x, y=x3, and x≥0.

A:

Q: Verify Green's Theorem by evaluating both integrals an aM dA y² dx + x² dy = |/ əx ду for the given…

A:

Q: Evaluate the line integral IF.då over the path C to Q (2,4) from P(0,) where F(xy) = 2xy2 + 3y f 131…

A: According to question, Given function, F→x, y = 2xy2 i^ +3y j^,We have to calculate line integral…

Q: Verify Green's Theorem by evaluating both integrals √( 1² dx + x² dy = √ √ (2x - 3M) JA dA əx ду for…

A:

Q: Verify Green's Theorem by evaluating both integrals v² dx + x² dy dA ax ду for the given path. C:…

A: This question is related to vector calculus solved in step 2.

Q: Verify Green's Theorem by evaluating both integrals [ 1² dx + x² oy = √ √ (2x - 3) da dA dy əx JR…

A:

Q: Evaluate the line integral along the given path. (4x-7y)ds C:r = 7ti+6tj, 0 ≤ y ≤8 O-454/85 O-444√85…

A:

Q: Set up the iterated (triple) integral for the integral ]]] xy¹z³ dV where S is the tetra- S hedron…

A: We will find limits of variable and then find value of integral

Q: Verify Green's Theorem by evaluating both integrals y? dx + x2 dy dA ду for the given path. C:…

A:

Q: Evaluate the triple integral,   4x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and…

A: To calculate the value of the triple integral under the given terms

Q: Evaluate the line integral by the two following methods. integral xy dx + x2 dy   C is…

A: The vertices of a rectangle 0,0,4,0,4,3 and 0,3. We have to evaluate the integral ∫Cxydx+x2dy.

Q: Evaluate the iterated integral. V 4 - y2 (x + y) dx dy

A: