10. Evaluate , (2x – y) dA where D is bounded by the circle with center the origin and radius 2.

Q: 4. Find the area of the plane region that lies below the line y = 2x and between the parabolas y =…

A: The area between two curves y=f(x) and y=g(x) within the x-limits x=a to x=b is given by:…

Q: Evaluate the line integral [6. 6ayⓇ ds, where C is the right half of the circle x² + y² = 4.

A: To evaluate :   ∫C6xy6ds, where C is the right half of the circle x2+y2=4 Prerequisite : We can…

Q: Compute the line integral (Баллов: 2) Jo ds, Cis the right half of circle x2 + y 16 (counter…

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Q: Let YR be the circle of radius R with counter clockwise orientation. Prove that 2 – 1 - lim R00 YR…

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Q: Evaluate the line integral xdy- xydx over the closed path C where Cis the circle C

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Q: Evaluate the line integral . xy ds, where Cis the top half of the circlex +y = 16.

A: The given integral is ∫C xy2 ds, where C is the top half of the circle x2+y2=16. To find: the value…

Q: 7. Use Green's Theorem to evaluate the integral f x²y dx - xy²dy where C: is the circle x² + y² = 4…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5) 2=2y, t at…

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Q: Show that [(x- y) dx + (x – y)' dy] = 3ra" taken along the circle x +y =a° in C the counter…

A:

Q: Find the area of the inner loop of the curve r= 1-2cos θ

A: For the inner loop of the curve 1-2cos θ=0⇒2cos θ=1⇒cos θ=12⇒θ=cos-112⇒θ=π3,5π3

Q: Use Green's theorem to evaluate O(1-y') dx+(x³ +e" ) dy , where C is the boundary of the region…

A: The integral is ∮C1-y3dx+x3+ey2dy where C is the boundary of the region between the circles x2+y2=4…

Q: 3) Find the area of the surface obtained by rotating the given curve about the indicated line, y=x2,…

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Q: dz The value of the integral Jc 22+9 where c is the circle z - 3i| = 4 is %3D

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Q: If  x=10cos^(3)⁡θ and y=10sin^(3)⁡θ, find the total length of the curve swept out by the point (x,y)…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)²=2y, the…

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Q: If the infinite curve y = e-6x, x > 0, is rotated about the x-axis, find the area of the resulting…

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Q: (1- y*)dx + (x° + e*)dy where C is the boundary of the region between the circles x² + y² = 4 and x²…

A:

Q: 3. Find the area of the surface generated by revolving the curve y = 2/x ,1Sx<2, about the x-axis(as…

A:

Q: What is the shortest distance from the surface xy +12x +z^2 =144 to the origin?

A: To find the shortest distance from surface xy +12x +z2 =144  to origin.

Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

A:

Q: Find the area of the region

A:

Q: c) Evaluate the line integral (x+2y)dx -2xdy along the following closed path, the circle x+ y= 25,…

A: In parametric form,

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

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Q: 23 + 3 4. Evaluate the integral dz, where C is the circle (a) |z + 3| = 3, (b) |z| = 3, (c) |z| = 7.…

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Q: # 4. Evaluate the line integral | (x +2x²y) ds, where C is the upper half of the unit circle x2 + y2…

A:

Q: Consider the region bounded by the Xxy curves J 3-2x, and y=3, %3D

A: Calculating the area of the region bounded by the curves

Q: 45. If A = (y – 2x )1 + (3x + 2y)j, compute the circulation of A about a circle C in the xy plane…

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Q: O By using Green's theorem, evaluate $ (In (2²) + æy² – y²) dæ + (ev + x²y – 3ry) dy, where C is the…

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Q: For the qutegradsSEddy tringle Over the bounded by -0,4=0 and *+y=l-

A: We have to find the integral  ∬e2x+3y dx dy   over the region R bounded by curves: x=0, y=0, x+y=1

Q: - x = 1 - y', x= y² – 1

A: topic - area bounded by curves

Q: Determine the osculating circle of the helix defined by y = x^3 − 3x + 1 at x = 1.

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Q: ⒸFind S (x- y²) dA, where I is bounded by the circle of D center (0,0) and radius 2.

A: As per as our guidelines i am supposed to answer

Q: 3. Evaluate the integral *zp- where C is the circle |2| = 2.

A:

Q: Let C consist of the part of the circle r +y = 4 from (2,0) to (0,2), Followed by the line segments…

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Q: By using Cauchy's integral formulas evaluate sin Tz2 + cos TZ² dz (z + 1)(z – 2) C and e2z dz (z –…

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Q: dr Let A be the area of a circle with radius r. If dt dA when dt 4, find %3D r = 3.

A:

Q: 3. Let D be the region bounded by the parabola y= -3 and the line y=1.F

A: The region is bounded by the curves given by: y=x2-3      and      y=1

Q: Q2 Calculate dz, - z) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: . SS, xcos(y)dA, D is bounded by y = 0,y = x² ,x = 1.

A: See the details solution in below

Q: Evaluate the line integral Levis where C is the half circle x² + y² = 1, y ≥ 0. x² + y² ds

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)²=2y, the…

A: Consider the circle, x2+y2=25 find the equation of the tangent line,…

Q: Evaluate the line integral ∫Cx2yds along the segment of the line y=x from the origin up to the point…

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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: Let YR be the circle of radius R with counter clockwise orientation. Prove that 1 -dz = 0. lim z3 +…

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Q: 4. Find the area of the surface generated by revolving the given curve about the -axis. y = 7x,0 <…

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Q: SS Q2: Evaluate (2x + y²) dA where R is the region in the R first octant bounded by circles x² + y²…

A: Introduction: When in a double integral, there is a region that is enclosed by circles, and it is…

Q: i Apply Green's theorem to eve luate S [rex=y)dx +Cx+g)dy], where C is the bocundaug qxis aiad the…

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Q: Calculate fSp(3x + 2y) dA where D is the region in the first quadrant that is inside the circle x2 +…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Evaluate the double integral. (8x – 6y) dA, D is bounded by the circle with center the origin and…

A: The given data is: ∫∫D8x-6ydA To evaluate the double integral.