Change the Cartesian integral to an equivalent polar integral, and then evaluate. integral from-2 to 2 and integral from square root 4-y2 to square root 4-y2 dxdy a)8pi b)16pi c)2pi d)4pi

Q: Find the area of the region Inside the cardioid r = a(1 + cos u), a > 0

A: Given  r=a1+cosu, a>0

Q: Evaluate, using Cauchy's integral formula: sin tz? + cos Tz? () dz where C is the circle |z| = 3 (z–…

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Q: Use Green's Theorem to evaluate the integral o (3x - y)dx + 4xdy where C is the circle x +y? = 1…

A: Consider the given integral. ∮C3x2-ydx+4xdy Here C is the circle x2+y2=1 The Green's theorem can be…

Q: Sketch the segment r = sec 0 for 0 < 0 < . Then compute its length in two ways: as an integral in…

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Q: Evaluate the double integral Answer: z²y dA, where D is the top half of the disc with center the…

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Q: Evaluate the given integral by changing to polar coordinates. 5x2y dA, where D is the top half of…

A: Please see the explanation below

Q: O Re(z) dz, where C is the circle |z| = 1 %3D

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Q: By using polar coordinate, evaluate Sl, x² + y² dA, if R is the region in between circle x² + y² = 1…

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Q: Evaluate the iterated integral by converting to polar coordinates: /25 – sin(a? + y?)dydx 5 Jo

A: We need to evaluate the following integral by converting to polar coordinates…

Q: Evaluate the double integral COs x² + y? dA, where D is the disc with center the origin and radius…

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Q: Using polar coordinates, evaluate the integral // sin(a? + )dA where R is the region 9 < 2? + 3? <…

A: The Cartesian coordinates (x, y) can be converted to polar coordinate system using the equation…

Q: Calculate the integral Se , where C is the unit circle Select one: O a. 0 O b. - 2 ri O c. 2 mi d. -…

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Q: Evaluate the given integral by changing to polar coordinates. 4x²y dA, where D is the top half of…

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Q: Assume a to be a nonzero real no.. Determine the area of the portion of surface xy = az in the fir…

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Q: Evaluate the integral eiz dz, (22 + 1)2 where C is the circle |2 + il = oriented anticlockwise.

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Q: 6. Use Green's Theorem to show that the area of the unit disk x2 + y? <1 in R? is T by evaluating a…

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Q: dzdydk 7A 1.

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Q: - Find the area of the negion that inside (i=3sin@) eind also In side (rz = + sin@) ?

A: To find the area of the region inside r1=3sinθ and inside r2=1+sinθ

Q: Evaluate the following integral by converting it into polar coordinates. |/ 2rydA, D is the portion…

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Q: Find the surface area generated by revolving the length of the arc of r = 1+ cose from o to Tt about…

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Q: Let C be the circle |2 – i| = 2 in positive sense. Use Cauchy Integral Formula to find: (a) Sc 74°…

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Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. /25-y (x² + y²)…

A: To convert this into polar for substitute:  x=rcos(theta)…

Q: Evaluate by De Moivre's Theorem and express the result in rectangular form.(5e^j1.222)^2

A: De Moivre's Theorem: einθ=cosnθ+isinnθ →     *

Q: Find the area contained in the cardiod using an integral in polar coordinates: r= Cos(0) +1

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Q: Evaluate the integral /R 2xy dA, where R is the triangle 4x + y 0, y 2 0.

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Q: The volume of the solid that lies above the cone θ=π4 and below the sphere r=cos(θ) is: (Here,…

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Q: (a) Let f(z) = 1 - 2i)(24 – 23) - 2 Using CRT, evaluate the integral Of(2)dz, where the contour C is…

A: 1. The point z=a is said to be an isolated singularity if there exists a number such that f(z) is…

Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. 9 81-x dy dx -9…

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Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. Nan 72 - y² Z+y²…

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Q: Use the polar coordinates to find the volume of a sphere of radius 3.

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Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. 7 149-x2 dy dx - 7…

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Q: Evaluate the given integral by changing to polar coordinates. /| 2x2y da, where D is the top half of…

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Q: Evaluate the double integral cos V x2 + y?dA, where D is the disc with center the origin and radius…

A: See the details solution in below

Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. dy dx 49-x2…

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: 1. The parts of spherical triangle are B=120°, C=150°, a=135°. What is the spherical excess? Compute…

A: We know: cos(A) = cos(a) sin(B) sin(C) − cos(B) cos(C)             =cos(135°) sin(120°) sin(150°) −…

Q: Evaluate the given Integral by changing to polar coordinates. || 2x2y dA, where D Is the top half of…

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Q: Evaluate the given integral by changing to polar coordinates. || 5x2y dA, where D is the top half of…

A: To convert integral into polar form then replace   .Also Change region D accordingly .

Q: Find the area of the region inside both the circle r=6 and the cardioid r=4+4cos(theta) (in other…

A: Given a circle and a cardiod in the polar form. We need to find the area inside the circle and…

Q: Evaluate the integral 1 V1-y² V2-x²– y² (x² + y? + 2?) dzdxdy 2+y² by changing it to spherical…

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Q: Evaluate the given integral by changing to polar coordinates. || 2x2y dA, where D is the top half of…

A: The given integral is ∬D 2x2y dA where D is the top half of the disk with center origin and radius…

Q: to find the aren ruse 2) Use a polar integral enclosed by the three-petaled r = singe

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Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. 9 81-x2 dy dx - 9…

A: We need to convert it into polar form

Q: Without evaluating the integral, show that z+4 67 -dz s 7. 2i +1 IC where C is the arc of the circle…

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Q: 2,5in. 2 in.

A: Please see the answer in Step 2 .

Q: Use polar coordinates to evaluate the integral d. where R is the region that lies in the second…

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Q: Show that 8r units is the length, L, of one arch of the cycloid described parametrically by: x (0) =…

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Q: 2-Change the Cartesian integral in to an equivalent polar integral, then evaluate polar integral (x²…

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Q: Find the areas of the regions Inside the oval limaçon r = 4 + 2 cos θ

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