5. Let R be the region in the first quadrant within the circle z² + y? = 4, outside the circle (z – 1)² + y² = 1, and between the lines y = 0 and y = r. Evaluate the double integral.

Q: 4/ Find the area of the region enclosed between the curves y= cos 2x, y=0, x=TT/4, x= TT/2 ? ans/…

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Q: verify Green's Theorem by evaluating both integrals * dx + x*dy = aM dA for the given path.

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Q: Use Green's Theorem to evaluate the line integral. (x – 2y) dx + (x + y) dy C: boundary of the…

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Q: 4. Evaluate S, cos dA where D is the region bounded by D = {(x, y)/ VL < x < v3Ln , 0 < y< x² }.

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Q: Calculate the double integral √ √(8x + 2y + 16) dA where R is the region: 0 ≤ x ≤ 1,0 ≤ y ≤ 4.

A: The objective is to evaluate the double integral.

Q: Evaluate the following integral: b.) !!!! xyz dv if S is the region bounded by the cylinders ² + y²…

A: According tot the given conditions the limi values of x,y and z are0≤x≤50≤y≤25-x20≤z≤25-x2Hence…

Q: (b) Verify Green's theorem for |(x² – 2x y)d x+(x² y+3)d y, around the boundary e of the region y…

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Q: ON Verify Green's Theorem by evaluating both integrals 7y dx + 7x*dy = J J]a дм ƏA for the path ду…

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Q: Use Green's Theorem to evaluate the line integral. |v² dx + xy dy C: boundary of the region lying…

A: Introduction: The line integral ∫CF·dr geometrically represents the circulation of the function F…

Q: Use Green's Theorem to evaluate the line integral Icov for the given path. (y-x) dx + (2x - y) dy C:…

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Q: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

A: Given: ∫Cy2 dx+xy dy, where C: boundary of the region lying between the graphs of y=0, y=x, and x=25…

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

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Q: Evaluate the line integral, where C is the given curve. (x + 8y) dx + x2 dy, C consists of line…

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Q: Verify Green's Theorem by evaluating both integrals aN dx + x² dy = / / dA ay y2 ax for the given…

A: To verify green's theorem by evaluating both the integrals.

Q: Use Green's Theorem to evaluate the line integral. dx + xy dy C: boundary of the region lying…

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Q: 2) Calculate the integral the regions descri bed. over / 2x- 5xy- 3y² dA. On a y = (x-1) /3 , y= -2x…

A: Bounding lines y=x3         → 3y-x=0y=(x-1)3→3y-x =-1y=-2x    →y+2x=0y=1-2x  →y+2x=1

Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x – y) dy for the given path. C:…

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Q: Use Green's Theorem to evaluate the line integral. | y2 dx + xy dy C: boundary of the region lying…

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Q: 3. Use Green's Theorem to evaluate (e3x +y²)dx + (sin y – x²)dy where C is the boundary of the…

A: Green's theorem

Q: 4. Evaluate fe cosy dx + (xy – xsiny) dy where C is the boundary of the region lying between the…

A: Given  ∫Ccosydx+(xy-xsiny)dy

Q: Evaluate the line integral, where C is the given curve. (x + 9y) dx + x² dy, C consists of line…

A: To evaluate the line integral, consider the curveC1 consisting of the line segment from0,0to9,1. The…

Q: Use Green's Theorem to evaluate the line integral. by² dx + xy c C: boundary of the region lying…

A: The objective of the question is evaluate the definite integral using Green's Theorem.

Q: 4. Compute the integral x sin (xy) dA where R is the region 0 <x <1 and 0<y < .

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Q: 5. Show that, in the region bounded by y = Vx and y = x2 the following double integral 3 (х + у) dA…

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Q: 3. Use a suitable change of coordinates to calculate the integral / x² – y² dA, where R is the R…

A: The region R is given by

Q: 2- Find D xyz dV where D is the region with -1 ≤x≤1, x ≤ y ≤ 1, above z = x, and below z = y + 2.

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Q: Evaluate the double integral 4.x dydr 9 + y2 I when A is the shaded region in enclosed by the graphs…

A: Evaluate the double integral.

Q: Use Green's Theorem to evaluate the line integral. √y² dx + xy dy C: boundary of the region lying…

A: We have to evaluate the integral.

Q: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

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Q: Evaluate the double integral / | y dA; R is the region in the first quad- R rant enclosed between…

A: O

Q: Use Green's Theorem to evaluate the line integral. J. 2xy dx + (x + y) dy C: boundary of the region…

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Q: Use Green's Theorem to evaluate the line integral (y – x) dx + (2x - y) dy for the given path. C:…

A: Use greens theorem

Q: 4. Evaluate the integral (a + y) dA; where D is the region bounded by y = and the line y = }- x.

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Q: Use Green's Theorem to evaluate the line integral √(x − x) dx + (2x - y) dy (y- for the given path.…

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Q: 4. Evaluate the double integral x cos y dA; R is the triangular region bounded by the lines y = x, y…

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Q: 21 Verify that (y² – 2x )dx +(2xy +x²)dy = || dA where C is the boundary of a region ôy -. R R…

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Q: Use Green's Theorem to evaluate (eš + y³)dx + (sin y – x²)dy where C is the boundary of the region…

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Q: Use an appropriate change of variable to evaluate the double integral: y- x cos y +x d A, R where R…

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

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Q: dV, where E is the region between two cylinders ²+², 5. Evaluate the integral and 2² +2²9 with 1 ≤ y…

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Q: Use Green's Theorem to evaluate the line integral. S y² dx + xy dy C: boundary of the region lying…

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Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: First I have changed the line integral into double integral with the help of Green's theorem and…

Q: What is the area of the region in the first quadrant bounded by the curves zy = 1, zy = 2 y= z, and…

A: We are give 4 curves: xy=1, xy=2, y=x, y=3x To find out: Area under these curves in first quadrant.

Q: Calculate the double integral ∬R(x2+y2)dxdy in the circle x2+y2=2x.

A: Write the equation of circle into standard form. The radius of the circle is 1.

Q: Use Green's Theorem to evaluate the line integral (у — х) dx + (2х — у) dy for the given path. C:…

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Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x - y) dy for the given path. C:…

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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: 4. Compute the value of the double integral fSRe-xydxdy, where R is the region bounded by the lines…

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Q: 8) consider the region R in the first quadrant(xz0, y2) bounded by x=2y² X=Y²+1 a) set up, but clo…

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Q: Evaluate // (1+x² + y2) dV, where E is the region bounded E by the surfaces z = 6y2 - 9x², and z = 6…

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