Q: Evaluate the line integral / Vxy° +3 dx +6xy" dy, where C any curve joining (1, -1) to (16, 1).
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Q: When transforming the triple integral a-st-y" (xZ+ y² + z²)ể dzdydx . 9-x2 9-X 2n n 3 to spherical…
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Q: 2. Evaluate the following double integral by switching to polar coordinates 16-y2 (16 – 22 – y*)…
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Q: 1. Use Green's theorem in order to compute the line integral $ (3cos + 6y?) dx + (sin(5") + 16x³) dy…
A: Here the given integral is ∮C3cosx+6y2dx + sin5y+16x3dy
Q: 1. Calculate the integral 1 y-stnx)dx + cosy dy a) With directly (classical), b) With the Green's…
A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…
Q: Convert the following double integral to polar coordinates (do not evaluate). 2 √√4-1² X dxdy = 1+…
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Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. S LvS- (x² + y²)…
A: Solve
Q: 3) Evaluate the iterated integral by converting the to polar coordinates -√₂x-x² a) √²ty² dydx…
A: Given that, The integrated integral: (a) ∫02∫02x-x2x2+y2dydx, such that , the region is…
Q: Question 3. Compute the integral dz 8+z where y is the rectangle with vertices +3+i with the…
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Q: Evaluate the iterated integral by converting to polar coordinates. 2х — х2 4 V x2 + y2 dy dx
A: Given that, ∫02∫02x-x24x2+y2dydx Calculate the integral value.
Q: 2x – x2 2х — х 5Vx2 + y2 dy dx
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Q: 4: Use Green's Theorem to evaluate the following integral e dx + (5x+ 6) dy Where C is the triangle…
A: Using green theorem to evaluate the following integral.
Q: Evalute the following integrals using Polar method: a √a²x² $5 Jy dx √a²-x²
A: An integral which involves the integration with respect to the product of the variables x and y is…
Q: Evaluate the following double integral by changing to polar coordinates. ey dydx
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Q: Evaluate the iterated integral. T/4 1 Tv cos(x) dy đx
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Q: Calculate $o (3x + 5y - cos(y)) dx + x sin(y) dy if C encloses a region of area 4.
A: To evaluate the given integral.
Q: 3. Evalnate. the.allowing.deuale.integral.by.conver.ting.bo. polar.Cta.r.dinates Co.fxdxdy Anse 3.6.…
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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…
A: Given: The given harmonics are Y1,+1=1232πsinθ e-iϕ and Y1,0=123πcosθ are orthogonal over the…
Q: 5. Evaluate the iterated integral by converting to polar co-ordinates: 1-y2 CoS V x² + y² dx dy
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Q: =H.w.2 Evaluate the following cartesian integrals by - changing them into equivalent Polar integrals…
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Q: Convert the integral to polar coordinates and evaluate. V49 - x2 sin(x2 + y2) dy dx V49- x2
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Q: (2) Evaluate the iterated integral by converting to polar coordinates. 1 √x-x² (x² + y²) dx dy [] 0…
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Q: 6] What is the Cartesian integral that represents the following polar integral r'sin e cos e dr de?…
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Q: 17. Change the Cartesian integral to an equivalent polar integral * --(x²+y?) dy dx e re -r dr d0…
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Q: Calculate the double integral. 9x sin(k + y) dA, R = 0, 풍핑x [o, 플]
A: First we will evaluate the inner integral wrt 'y' and then evaluate wrt 'x'.
Q: Evaluate the iterated integral by converting to polar coordinates. '2 2x – x2 4V x2 + y2 dy dx 0.
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Q: Evaluate the iterated integral. '1 cos(s³) dt ds Jo Jo
A: Given- ∫01∫0s2coss3 dtds To evaluate- The iterated integral.
Q: Evaluate the line integral (cos x + sin y) ds; C is the line segment from (0, 0) to (x, 67).
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Q: 6] What is the Cartesian integral that represents the following polar integral fr' sin e cos e dr de…
A: Let x = r cos(theta) y = r sin(theta).
Q: Evaluate the following integrals in polar form V4-y (x2 + y2) dx dy a- b- y dy dx C- dx dy d- dy dx…
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Q: Evaluate the Iterated integral by converting to polar oordinates. .V 2x – x2 8V x2 + y2 dy dx
A: Given that The double integral To evaluate the integral by using polar coordinates
Q: √1-y² If ²₁¹² x² + y² dxdy is changed to equivalent integral in polar coordinates, then the…
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Q: (2) Evaluate the iterated integral by converting to polar coordinates. 2 v8-yz Vx2 + y² dx dy o y
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Q: 9-x2 C: Change to polar and evaluate the double integrals S (x3 + xy?)dydx V9-x2
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Q: 1)Evaluate the interated integral by converting to polar V4-x2 x2+y2 dydx xpáp_zh + z*\ ITV
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Q: Question 3. Compute the integral - dz 8+z where y is the rectangle with vertices +3+ i with the…
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Q: 2 9-x sin (x? +y² ) dy dx 2 sin x +y 2 9-x 3.
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Q: Evaluate the iterated integral by converting to polar coordinates. 2x – x2 8V x2 + y2 dy dx
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Q: 2. Express the iterated integral as a double integral in polar coordinates. 1 X 1 Lo dy dx 16/2 x² +…
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Q: Use Green's Theorem to evaluate the line integral. et cos(2y) dx 2ex sin(2y) dy C: x2 + y2 = a?
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Q: 3) Evaluate the iterated integral by converting the to polar coordinates . - √x²+y² dy dx (۹۰) ره ۹)…
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Q: 16–x² Choose the iterated integral that is equivalent to y dy dx in polar coordinates.
A: let x=rcosθ and y=rsinθ dydx=rdrdθydydx=r2sinθdrdθ 16-x2=yx2+y2=42=r2 r=4 Therefore r varies from 0…
Q: 2. Convert the following double integral to polar coordinates and evaluate. S so dx dy 4y-y² Jx²+y²…
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Q: Use Green's Theorem to evaluate the line integral below. √ (x² − y²) dx + 7xy dy C:r = 1 + cos(8), 0…
A: Given integral is ∫Cx2-y2dx+7xy dy where C: r=1+cosθ, 0≤θ≤2π To Use: Green's Theorem to evaluate…
Q: Evaluate the double integral: cos(y') Vy3 dy dx.
A: The solution is given as
Q: /4-y2 1 dx dy 1+x2 +y2 0.
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Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. (9-x2 3 s S - 3…
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Q: Consider the double integral I = J .3 cos(x² + y²) dydx. By converting I into polar form, the limits…
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Q: Evaluate the integral: L x2 + y² dy dx by using polar coordinates.
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- Use polar coordinates to integrate under z=xy above the first quadrant of the unit circle on the xy plane?2. Chapter 15 Review 33: Use polar coordinates to calculate sD√x2 + y2dA where D is the region inthe first quadrant bounded by the spiral r = θ, the circle r = 1, and the x-axis.1. How many petals does the polar curve r=5cos(6theta)? 2. At what points the curves r=4sin(2theta) and r=4cos(theta) intersect?
- Suppose that U is a solution to the Laplace equation in the disk Ω = {r ≤ 1} andthat U(1, θ) = 5 − sin^2(θ).(i) Without finding the solution to the equation, compute the value of U at theorigin – i.e. at r = 0.(ii) Without finding the solution to the equation, determine the location of themaxima and minima of U in Ω.(Hint: sin^2(θ) =(1−cos^2(θ))/2.)Given two polar curves and r=2cos2θ , r =1 as in Figure 1. Find the area of the shaded region by using the single integration in polar coordinates.Which of the following is the surface area of the solid body created by rotating the given parametric curve around the x-axis?
- Find the areas of the regions . 1. Shared by the circle r = 2 and the cardioid r = 2(1 - cos u) 2. Shared by the cardioids r = 2(1 + cos u) and r = 2(1 - cos u)Give a parametric representation for the cylinder x^2+z^2=121A torus of radius 2 (and cross-sectional radius 1) can be represented parametrically by the function r:D→R3:r(θ,ϕ)=((2+cosϕ)cosθ,(2+cosϕ)sinθ,sinϕ)where D is the rectangle given by 0≤θ≤2π, 0≤ϕ≤2π.The surface area of the torus is