27. Evaluate the iterated integral. xy² a) SS₂ 2²x dA where R = {(x, y): 0 ≤ x ≤1,-1 ≤ y ≤ 1} b) ₁₂² ye xy da where R = [0, 1] × [0, 2]

Q: Evaluate the line integral feF. dr where F = (4 sin x, -3 cos y, 5xz) and C is the path given by…

A:

Q: 23. Evaluate the iterated integral. f²f (6x²y - a) (6x²y - 2x) dydx ») ff ² (4x² – x²y³²) dydx

A: Definite Integral

Q: -x + 2 dx . x2 + 2x ate the integral

A:

Q: 1. Find V · (V × F), for F(x,y, z) yzi + xzj + xyk.

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: B- Evaluate the integral 1-x (3-x-y dz dy dx /1-x²

A:

Q: 3. Evaluate the double iterated integral || y dA where R is the finite triangle bounded by the…

A:

Q: Calculate the line integral f(3xy³ − 4x + 4y + 8) dx + (−3xy+5) dy, where C' is the rectangle with…

A:

Q: find √x² ds along the line of intersection of the two planes X-Y+z = 0 and x+y+ 2z =0, From origin…

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Q: c. Integrate the function f(x, y) = x-y over the triangle with vertices (0,0), (1,0), and (2, 1). Do…

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Q: Evaluate S ○ In O Divergent ○ In 11 O 6 In 11 6 dz 2²-25 16

A: Given problem :- ∫6∞6x2-25dx

Q: 1. Evaluate the integral If. (430 R (4x + 16y)dA, where R is the parallelogram bounded by the lines…

A: To find the given integral , we can change the given integral in  terms of 'u' and 'v' .

Q: Evaluate the line integral. -y dx + x dy segment from (3, 0) to (0, 3) x2 + y2

A: Find the slope of the line through the given points.

Q: .2 Evaluate the line integral xy dx + x-dy, where C is the path going counterclockwise around the…

A: Given, ∮Cxydx+x2dy, Where C is the path going counterclockwise around the boundary of the rectangle…

Q: 1. Consider the lune enclosed between x² + y² = 1 and x² + (y+1)² =2. Show the following using…

A:

Q: 3 1 4 1 | |(2x – 4y)dydx (2х — |x²ydxdy 3. 4. - 1 2 0 2π π |(sinx + cosy)dxdy 5.

A:

Q: P. 2. Evaluate the triple integral S' L___7z S"'¹m(1 + √2² + y² + z2²)dzdydr. 0

A: Consider the integral as The objective is to evaluate.

Q: Evaluate the line integral -ydx + xdy along the curve C : y = 3x from (3, 3) to (0,0). NOTE: Enter…

A: We have to find the line integral ∫C-ydx+xdy along the curve C: y2=3x from (3,3) to (0,0)