Prove that (x,y,z)=(2.25,-1.35,0.169) minimizes 1.5 the integral , [w3 – (xt² + yt – z)]² dw

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

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

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Q: Find the line integral of f (x, y,z) = -x + y + z over the straight-line segment from (1, 2, 3) to…

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Q: Suppose that f (x, y) = y/x³ + 1 at which {(x, y) | 0 < y < æ < 5}. Then the double integral of f(x,…

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Q: Suppose that f(x, y) 2æ + 4y on the domain D = {(x, y) |1< x < 2, x² < y < 4}. D Then the double…

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Q: Evaluate the triple integral. 2xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

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Q: Q3: What is the answer of the double integral of the f (x, y) = 4x+2 over the region x^2<ys2x, and…

A: According to question, Given function,fx, y = 4x+2,x2 ≤y≤2x,0 ≤x ≤ 2

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

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Q: Suppose that f(x, y) 3, and D = {(x, y) | æ² + y² < 16}. Then the double integral of f(r, y) over D…

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

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Q: Suppose that f(x, y) = at which 1+ x {(x, y) | 0 < x < 4, – x < y < VI}. D Then the double integral…

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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: Evaluate the line integral by two methods: (a) directly and (b) using Green’s Theorem.3. ∮C xy dx +…

A: According to Greens theorem :

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:…

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

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Q: (a) Compute the multiple integrals of (i) V4-z2 1 xy dxdydz (11) SS, (8 – x² – y²)dA, where R = {(x,…

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Q: 1. Give iterated integrals for r (x² + yz)dV where E is in the first octant bounded by the planes: y…

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Q: Evaluate the line integral of x^3(z)ds, where C is the line segment from (0,8,2) to (7,4,6).

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Q: Evaluate the integral (x + z) dS where S is the part of the cylinder y + z2 = 4 with x E [0, 9].

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Q: Evaluate the double integral. // (x2 + 2y) dA, Dis bounded by y = x, y = x³, x > o

A: To evaluate the below double integral ∫∫Dx2+2ydA ,   D is bounded by y=x, y=x3,x≥0

Q: Q3: What is the answer of the double integral of the f (x, y) = 4x+2 over the region x^2sys2x, %3D…

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Q: Evaluate the double integral using single applications of Simpson's 1/3 rule 2 (x2. 3y2 + xy³) dx dy…

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Q: Suppose that (x, y) = x+ 4y on the domain D = {(r, y) | 15x< 2, x? sys4. D Then the double integral…

A: Given that, f(x, y) = x + 4y and   {1≤x≤2},  {x2 ≤y≤4} We have to calculate the value of ∬Df(x, y)…

Q: Suppose that f(x, y) 4 - a? - y and D = {(x, y) | 2² + y² < 4}. Then the double integral of f(x, y)…

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Q: Suppose that f(r, y) = 2x + 4y at which {(x, y) |-1<a < 3, - 1<y< 3}. Then the double integral of…

A: ∫∫Df(x,y)dx dy=∫∫D2x+4ydx dy=∫-13∫-132x+4ydx dy=∫-13∫-132x+4ydx dy=∫-13x2+4xy3-1…

Q: Suppose that f(r, y) = 1 on the domain D = {(x, y) | – 3 < ¤ < 2, – 3 < y < 2}. D is Then the double…

A: Given function:fx,y=1.And the given domain D=x,y|-3≤x≤2, -3≤y≤2We need to find the double…

Q: evaluate the triple integral given by fff (x + 2y)dV, where E is bounded by the cylinder y = x² and…

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Q: Suppose that f(æ, y) = yVæ³ + 1 on the domain D = {(x, y) | 0 < y < x < 1 D Then the double integral…

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Q: Find y(x) that minimized the integral | using the end conditions y(0) = 0 y'(1) = 0 %3D

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Q: Verify the Green's theorem for integral x²y dx + xy dy, where C is the boundary described…

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Q: Evaluate the double integral. [[ ×20 (2+2y) dA, D is bounded by y = x, y = 2³₁x20

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Q: Find the line integral of f(x,y,z) = -x+y+z over the straight-line segment from (1, 2, 3) to (0, −1,…

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Q: Suppose that f(x, y) at which {(x, y) |0 < x < 3, – x <ys vã}. 1+ x D Then the double integral of…

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Q: Suppose that f(x, y) = 6, and D = {(x, y) | x² + y² ≤ 4}. I Then the double integral of f(x, y) over…

A: Explanation of the answer is as follows

Q: Find the line integral of f(x,y,z) = x+ y+z over the straight-line segment from (2,1,3) to (1, –…

A: Solution: f(x,y,z)=x+y+z

Q: Justify the Fundamental Theorem of Line Integrals for F. dr in the case when F(x, y) = (8x + 8y)i +…

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Q: 4. Evaluate the integral f. x'y°dy – x5y'dx, where C is the square determined by the 0, y = 0, x =…

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Q: Calculate the double integral: S,(y + xy – 2) dA where R= [0,2] x [1,2].

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

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Q: at is the ans

A: Introduction: Integration is a method of bringing separate parts to form a whole. We find a function…

Q: Use the Fundamental Theorem of Line Integrals to evaluate fo F·dR, where F(x, y) = (x²y² – 3x, r³y)…

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

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Q: Suppose that f(æ, y) = 7, and D = {(x, y) | x² + y² < 1}. Then the double integral of f(x, y) over D…

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Q: Suppose that f(x, y) = 6, and D = {(x, y) | x² + y? < 4}. Then the double integral of f(x, y) over D…

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Q: Suppose that f(, y) = 4x + 5y at which {(r, y) | – 3 <I < 5, – 3 < y < 5}. D Then the double…

A: Integration is the calculation of an integral, which is used to find volumes, areas etc.

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: O Evaluate the line integral over The Cur ve C. SCx+y+2)dx +6x +y-2)dy+ (x-y+2)dz where c is the…

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

A: Consider the following graph:

Q: Suppose that f(c, y): at which {(x, y) | 0 s< 1, - a <yS vE}. 1+ x Then the double integral of f(x,…

A: According to question given that f(x,y)=y1+x at which {x,y) |0≤x≤1, -x≤y≤x