(15) Evaluate the integral if F(x, y, z) = (z, y, z) and S is given by r(u, v) - (u cos v, u sin v, u) over the region D given by 0 ≤ u≤ 1,0 ≤v ≤ π. Hint: Use the formula //F = [[F(x(u, v)) - F₁ × Fv F.dS F.dS= dA

Q: Let a(z, r) := 2+ re", te (0, 27). Calculate the following integrals: a) Sa-a sin(=) dz; sin(s) b)…

A: Given:                    αz,r:=z+reit, t∈0,2π To find: Evaluate the given integrals over the given…

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

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

A: Definite Integral

Q: S. V*(x+1) dx 13. Evaluate the integral: 16 A. 0 В. 1 C.- 5 D. 2

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: f(x, y, z) = z(x² + y² + z²)-3/2 over the part of the ball x² + y² + z² 2.5

A: Here we will use cylindrical co ordinate system to find value of integral  By using above figure…

Q: 24 dA - I 3x – Y when D is the parallelogram bounded by x – 2y = 0, x – 2y = 2, - and Зх — у 3D 1,…

A:

Q: Indicate whether the following statement is true or false. Let f (x, y) be any real valued function…

A:

Q: 1- Assume that x, y ER and z = x+ iy e C. Calculate the following integrals on C = {z: |z| = 1}…

A: Cauchy integral formula

Q: Incorrectly, we usually say that when we multiply any number by ten we “add” a zero to the number.…

A: a) Jushua is wrong because the correct answer is 10×1.3=13 b) If a whole number is multiplied by 10…

Q: Let f= 2zy + yx, v= [y, z, 4z -x]. Find Dyf at (2,1,2). NOTE: Enter an exact answer. Dvf (2, 1, 2) =

A: Given: fx, y, z=2zy+yx, v=y, z, 4z-xTo find: The directional derivative, Dvf at 2, 1, 2

Q: Given a rate of 175 pesos per hour, how many hours should you work to earn 35,962.50 pesos

A: If ∆x is the amount earned in time ∆t, then the equation for the rate of the amount earned per unit…

Q: Q6) valuate the integral as f(x, y, z) = (1+ rks) = cos(2t) i+ sin(2t)j+ tik ;0sts 2n.

A:

Q: What is the value of the line integral ∫ AB y dx + x dy, if x = 3*t, y = 4*t + 4 and 0 ≤ t ≤ 1?

A: I am solving this in step 2

Q: Evaluate the integral f, (5x + 6y²) dA, where R = {(x,y)|0 < x < 4,0 < y < 3}.

A: Given integral is ∬R (5x + 6y2) dA Where R =  (x, y) | 0≤x≤4, 0≤y≤3

Q: The graph of fis shown. y y= AX) 10 10 20 30 40 Evaluate each integral by interpreting it in terms…

A: "Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: Verify Green's Theorem by evaluating both integrals v? dx + x? dy = . dA дх ду for the given path.…

A:

Q: F(x, y, z) = (2xe*) i+ (2y + 3y?22)j+ (x²e* + 2y³z) k is conservative. Find a functionf such that F…

A: To find the function f  And then evaluate the line integral along the given curve.

Q: 1. Let f(x, y) = x cos (x²y). find: af a) ƏH b) of evaluated at (s) our (show you work)

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Q: If the change of variable |ə (x, y) d(u, v) | v v³ (²) = (²+²) u at the point where (x, y) = (2, 3)?…

A:

Q: Compute The integral f the scalar funetion over r (t)= bxy+32 %3D f(x,yd= ? 3.

A: Given curve is r(t)=cost,sint,tx=cost, y=sint, z=tdxdt2+dydt2+dzdt2=(-sint)2+(cost)2+1=2

Q: C is the curve y = e® from (2, e²) to (0,1) and F = (x², -y), compute ſ, F-dr.

A: Given that, C is the curve y=ex from 2,e2 to 0,1 and F=x2,-y Then, F=x2,-y=x2,-ex So, F→=x2i^-exj^

Q: Find the line integral where C is the semicircle y = A. I = 96 B. I-160 80 162 traversed from (4,0)…

A: