Consider the double integral (x +1)² + (y – 1)? = 2 R R Where R is the regron of Xy given Find the integral aPRlng variqble in "polar' form aange of 7/4 2² + y? = 4 A) I= r cos e drde + r cos e drde T/4 2(sin 0-cos 0) n/4 B) I = cos 0 drdo + cos 0 drdo Jo /4 7/4 ra/2 C) I = r cos 0 drdo + r cos o drdo */4 D) I = cos e drde cos e drde 2(sin 0-cos 0)

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Q: 10 Use the fundamental theorem to evaluate the following integras 1+2i (a) cos3z dz S ze*, (b) (c) J…

A: Dear Learner,we can solve only three subparts as we are following Bartlbey Experts Guildlines to…

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Q: 6. Consider the limnaçon curve with polar equation r = 2 cos 0 – 1 for 0 < 0 < 2n. (а) Set up (but…

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Q: Show that the spherical harmonics 1 3 sin 0 e-iº, 2V 27 Y1,+1 and 3 1 Y1,0 2V V cos 0, %3D | are…

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Q: 2. Set up a double integral using polar cor r=4sin 30. Do not evaluate. nates that will yield the…

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Q: 5. Calculate the double integral f, 2x cos(xy) dA , R = [0,2] × [0, 7]

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Q: 1 Change the double integral J. dydx into polar integral. 4-x² x² + drde drd0 drde 2[-drde or

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Q: At the point of discontinuity on (0, co), the Fourier Cosine integral corverges to: f(x+) – f(x¯)]…

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Q: Evaluate the following line integrals in the complex plane by direct integration (not using…

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Q: 48.) Find work done by F (2x³y* + x, 2x*y³ + y) along the path r(t) = (t cos(nt) – 1, sin (t)) 0sts1…

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Q: Show that+ = 0, %3D ax dy? where f(x, y) = In(x² + y²) + tan¯'(²) %3D

A: The partial derivative of a two variable function fx,y with respect 'x' can be calculated by…

Q: Consider the double integral 9-x2 dydx. By converting to polar coordinates, 2 the limits of…

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Q: 2. Evaluate the integral by first converting into spherical coordinates: |4–x² 4-x² J2-. r2+/4-x²-y²…

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Q: Calculate the area bounded by r = 2 cos 0 and the rays 0 = 0 and 0 =7 as an integral in polar…

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Q: Using double integral in polar coordinates, compute the following: raldorg somnlor guiwellolailt…

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Q: 3. Find the area of the region that lies inside both curves: r = sin 0,r = cos 0 0.8 0.6 0.4 0.2…

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Q: 2. Evaluate O (2y + In(5x² +3)) dx + (10x 3) dy along the boundary of the elliptic- region 4. y? 1…

A: Introduction: Green's theorem is very efficient in calculating line integral. When the line intgeral…

Q: 9-x2 Consider the double integral dydx. By converting to polar coordinates, the limits of…

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Q: 2/ Find the line integrals of the ellipse+3= ellipse by x = acos(t) ,y= bsin(t) 1 , parameterize the…

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Q: 8.) Find work done by F = (2x³y* + x, 2x*y³ + y) along the path r(t) = (t cos(at) – 1, sin (t))…

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Q: 3. Consider the line segment L = [-1-i, 1 + i]. Calculate the value of the integral 1₁² z² dz.…

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Q: aluate the iterated double integral. 1 cos(y) /5 + cos² (y) dydx Saresin (2)

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Q: Compute the integral using contour integration: 27 cos no (cos 0+a)20 for a > 1.

A: Note:- ∫C fz dz =2πi ×sum of residues cosnθ= Re ei nθ  cosθ=ei θ+e-i θ2      Given that  ∫02π…

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Q: (Compute Sc (-3y+ony Sin(3))dxt (5x²-(ye)du Where C is a Simple Clased cUne in the plane oriented…

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Q: Use symmetry to evaluate the double integral. 10 sin(x) dA, R = [0, 2n] × [0, 21]

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Q: b) Evaluate the integral using polar coordinates: 2x-x² So So x dydx 0

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Q: Use residues to evaluate the integral 2T 1 de. %3D 5+3 cos 0

A: To evaluate : ∫02π15+3 cos θdθConsider unit circle |z|=1i.e. z=eiθ⇒dθ=dzizAlso, we use cos θ=z2+12z,…

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