Evaluate the line integral ſe ry²ds, where C is three quarters of the circle a² +y? = 1, oriented counterclockwise (so the path of the circle from (1,0) to (0, –1)).

Q: Find the integral surface of the linear PDE xp - yq = z which contains the circle x² + y? = 1, z=1.

A: From Lagrange method

Q: Use Green's Theorem to evaluate the line integral ∫c ( x − y ) dx + ( x + y ) dy where C is the…

A:

Q: Let C be a circle lying in the plane x+ z = 2 with center at (1,0, 1). Evaluate the line integr V2…

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Q: Evaluate the line integral [(x+ y)dx+(x - y)dy, where C is the arc of the parabola y = 2x from (0,…

A: The integral in the form ∫CM(x,y)dx+N(x,y)dy involves the integration over a specific path C. In…

Q: Compute the line integral (х — y) dx + xe x dy, where C is the closed curve consisting of two line…

A: line integration

Q: Evaluate the line integral g. y² dx – x²dy, where Cis the positively oriented circle of radius 2…

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Q: Use Green's Theorem to evaluate the line integral f(e*c - 2y)dx+(5x+ev* dy, where C is the 15. 2cos:…

A: We need to find integral.

Q: Evaluate the following line integral | 2ry da + 42°y² dy along positively oriented circle with…

A: Let C is a counterclockwise oriented simple closed curve with the interior region R. According to…

Q: 4. Evaluate the line integral 6. x²y dx – xy² dy where C consists of the arc of the circle 16 = x² +…

A: Given equation of circle is  x2+y2=16x2+y2=42 radius is 4 We have to calculate line integral ∮ cx2y…

Q: The foilowing describes a para bolic path C: Pt) = (t, 2, 1-t?) %3D if F = (32, x + y+Z, 2x >,…

A: The given problem is to evaluate the line integral of the given vector field over the given…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. ∫C…

A: by usingGreen's Theorem to evaluate the line integral along the given positively oriented curve.…

Q: Compute the line integral -xdy + ydx 2(x-y)2 + 4xy where L is the circle (1-x)2 + y? 3 with a…

A: We will find parametric equation of L and then convert whole equation in parametric form

Q: Evaluate the integral | (3x – 2 y + :)ds where C is the curve, C, and C, as shown. 3- y² + z² 2. 3…

A: Here, Curve C is equivalent to c1+c2. The point of intersections of c1 and c2 is at 0,1,0.

Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

A: Greens theorem states that "for closed curve C enclosed a region R then the line integral along the…

Q: Use Green's Theorem to evaluate the integral (x² - y)dax + 3xdy where C is the circle x² + y² = 1…

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Q: Evaluate the line integral, where C is the given curve. xy ds, C is the right half of the circle x2…

A: C is the right half of the circle x2+y2=16 thus the parameterization of the circle is x=4cos t and…

Q: Use Green's theorem to evaluate the line integral r ry dr+r² where C is positively oriented curve…

A: Introduction: The process of determining the area of the region under the curve is known as…

Q: Evaluate the line integral, where C is the given curve. Lexy² ds, C is the right half of the circle…

A: Solution: I=∫cxy4ds

Q: Calculate Se(5x + 3y) i + (4x + 3y) j) · dĩ where C is the circular path with center (a, b) and…

A:

Q: • Use Green theorem to evaluate the Line integral $(x-3y) da +(42+y) dy whe re C, the Yectungle with…

A:

Q: Evaluate the line integral g. y³ dx – x²dy, where C is the positively oriented circle of radius 2…

A: Solved below.

Q: Let C be the positively oriented circle centered at the point zo with radius r>0. Use a…

A: We will first parametize the circle C

Q: Use Green's Theorem to evaluate the line integral F.dr, where F(x, y) = (x√√x+y₁x² + √√) and C is…

A: Here we have to apply greens theorem.

Q: Evaluate the line integral - y)dz + (1+ } + æ*)dy, where C is the circle of radius 1 centered at the…

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Q: Evaluate the line integral, where C is the given curve. | xy? ds, C is the right half of the circle…

A:

Q: Evaluate the line integral 2xyz dx + x²z dy + x?y dz where C is an oriented simple curve connecting…

A: Given line integral is,

Q: Use Green's Theorem to evaluate the line integr y? dx + x • when C is the circle of radius 2…

A: Introduction: Let C be a positively oriented, piecewise smooth, simple, closed curve, and D be the…

Q: Evaluate the exact area of the surface obtained by rotating the circle x2 + y² = r² about the line y…

A:

Q: Find the integral fc ez dz where C is the circle |z| = 3 in CCD. (z – 1)2(z – 2) %3D -

A:

Q: : The curve C is intersecting by 12r² +9y? = 36 cylinder and - V3r plane from the point (0, 2,0) to…

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Q: Evaluate the line integral f. y³ dx – x³dy, where C is the positively oriented circle of radius 2…

A:

Q: Evaluate the integral xy ds, where C is the curve consisting of the portion of the unit circle of…

A: The given integral is ∫Cxy ds where C is the curve consisting of the portion of the unit circle…

Q: Evaluate the integral | xy ds, where C is the curve consisting of the portion of the unit circle of…

A: Let us assume thatC1:x2+y2=1Put x=t,y=1-t2 and z=0.Hence,dx=dtdy=-t1-t2dz=0and 0≤t≤1.Let C2:The line…

Q: Let F (tan-(3x) + y)i + (2x + sec-ly)j and C be the boundaries of the %3D circle x? + (y- 4)2 = 9 in…

A:

Q: Evaluate the line integral fx ds between (4,0) and (0,4), where C is the circle of radius 4 centred…

A:

Q: Evaluate the line integral G. dr with G(x, y) = xyi+ 2y² j, and C is the closed path comprising the…

A:

Q: Evaluate the line integral ſc(4y+ tan? x)dx + (6x – evsin´y)dy over curve C that is the circle x2 +…

A: Green's theorem problem....

Q: 4. Let C be the positively oriented circle centered at the origin with radius r> 3. Without…

A: Given: Let C be a positive oriented circle centered at the origin with radius r>3. Without…

Q: Compute the line integral f, x?dx + y²dy where the path C consists of the arc of the circle x? + y?…

A: Here we solve the given problem of integral.

Q: Evaluate the line integral § (x − y) dx + (x + y) dy, where C is the circle with center the origin…

A:

Q: Compute the line integral Sy?a dl where y is the part of the circle centered at the origin and of…

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Q: Evaluate the line integral, where C is the given plane curve. xy ds, C is the right half of the…

A:

Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

A: Greens theorem

Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

A:

Q: 3. (a) Use Green's theorem to evaluate the line integral 4 y* dx – a* dy where C is the positively…

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Q: the line integral SexY² ds where C is the of the Circle x² + y²=4 oriented clockwise Evaluate Cight…

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Q: Evaluate y dx+3xy dy, where C is the boundary of the semiannual region D in the upper half-plane…

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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.

Q: Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant. (Use…

A: Part of the plane equation   5x+4y+z=20⇒z=20-5x-4yPlane lies in the first octant , so x≥0 ,…

Q: Evaluate the line integral: x dy – y da x² + y² where C is the circle x² + y? = a², a > 0, oriented…

A:

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.