Explain why the element of area in Cartesian coordinates dx dybecomes r dr dθ in polar coordinates.

Q: Find the area of the interior of the four-petaled rose r=sin(2θ)

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Q: Find the area of the cardioid r = 4 + 3 sin theta that lies in Quadrants I and IV.

A: Given the cardioid that lies in the 1st and 4th quadrant

Q: 2 Convert this ntegral From rectangular Coordinte to Spherical Coordina tes (Donot eval vate the…

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Q: Convert to spherical coordinates. √9-x2 3 St. Sort So √x² + y² [x² + y² (1) Z aretan, dzdy dx

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Q: Which of the following is the surface area of the solid body created by rotating the given…

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Q: Use spherical coordinates to evaluate 2π FT S 2-r r+z 0 (r² +2²) ³/ rdz dr de.

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Q: Use polar coordinates to evaluate r3 /9-x² I (a² + y°) dy dar. x (x2 V9-x²

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Q: Convert to polor coordinates with  r ≥ 0 and 0 ≤ theta < 2pi (4,0)  (r, theta) = ?

A: Polar coordinates (r, θ)            where r ≥ 0 and 0 ≤ theta &lt; 2pi Cartesian coordinates (x, y)…

Q: rm (r, "/3) fron polar into rectangula Iorm any posit radius

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Q: Find the area outside "r^2=9cos(2theta)" and inside "r=2-cos(theta)"

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Q: Use the previous exercise to write the equation of the circle ofradius 5 and center (3, 4) in the…

A: Standard form of a equation of a circle whose center is (h, k) and radius is r is, x-h2+y-k2=r2

Q: Calculate the value of x in the figure: AB = BC = DA and BD = DC (Not drawn to scale). %3D %3D 21 2x…

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Q: Which of the following correctly changes the integral rdrde from polar coordinates to rectangular…

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Q: EX, chang to polar and evaluate I= f dy hpxpx

A: Find Your Solution Below

Q: Integrate by changing to polar coordinates. (4 - x2 tan V 4 -1(Y) dy dx

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Q: osen y

A: Is it sen y =x

Q: Convert the following to rectangular coordinates and spherical coordinates. Do not evaluate the…

A: Given: The Tripple integral is ∫02π∫02∫r4-r2r2θdzdrdθ. To convert: The integral into the rectangle…

Q: How do you find the area of a polar regionR = {(r, θ): g(θ) ≤ r ≤ h(θ), a ≤ θ ≤ β}?

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Q: Derive the formula cos(a)=cos(b)cos(c)+sin(b)sin(c)cos(A) for an arbitrary spherical triangle with…

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Q: Change from Caresian to Polar and evaluate 7 J49-xa SS dy dx -1 0

A: The objective is to change the integral from cartesian to polar and evaluate the integral..

Q: Converted into polar coordinates, the integral r1/2 1-y L" Pydzdy becomes Select one: r3 cos? 0 sin…

A: We will first identify the region of the integration then we will obtain the limits in polar…

Q: (a) Use polar coordinates to evaluate [[ Jx? + y? dA, where R is the region inside the circle (x–…

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Q: Use Green's Theorem to calculate (4z? - 3yz)dr + (3zy + Vy? + 6)dy, where Cis the circle (r – 1)2 +…

A: Given: ∮C4x2-3yxdx+3xy+y2+6dy, where Cis the circle x-12+y-22=4. Greens theorem: Let C be a…

Q: Use the parametric equations of an ellipse x = acos(theta), y = bsin(theta) on the interval[0,2pi]…

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Q: Convert to spherical coordinates and evaluate: 4-x2-y2 4-x2 -4²+x²+z?)² dzdy dx

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Q: 3 Use Green's theorem to evaluate [x³y dx - xy²dy, where C C is the unit circle x²+y=1 with…

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Q: Find the polar equution for the cartesian curve r=8 sin o Cos o r=8 sec e tan E r=8 sine tan E r=8…

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Q: Verify that dV = p sin o dp de dy when using spherical coordinates. %3D

A: We have to represent a differential element.

Q: dV , where V is the unit sphere.

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Q: Use polar coordinate to evaluate (x² + y* )² dx dy . Leave your answer correct to two decimal…

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Q: Use polar coordinates to integrate under z=xy above the first quadrant of the unit circle on the xy…

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Q: Find the area shared by the circle r=1 and r=2cos(theta)

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Q: Use the parametric equations of an ellipse, x = a cos(0), y = b sin(0), o sos 2r, to find the area…

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Q: tind the area of the parametric curve X = t ,4=9t-73

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Q: 4. y = sin2r, 0 sa Find the area of the surface of rotation obtained by rotating the curved segment…

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Q: Find the area of the rigion lies between the circles r=2 and r=4cos(theta) in the first octant.

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Q: Find the area inside the oval limaçon r = 6 + sin 0.

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Q: find the area of the Shaded Part AUsing Polar y =2X

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Q: Determine the surface area of the object obtained by rotating r = cos 8,-303% about the y-axis.

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Q: Find the polar moment of inertia of the shaded area about the axis perpendicular to origin of the…

A: Answer is mentioned below

Q: Use Green's theorem to evaluate $y – sinx)dx + cosx dy Where c the triangle of the adjoining figure…

A: Green`s Theorem:-  Green`s Theorem states that the line integral is equal to the double integral of…

Q: What is the area of the region enclosed by the polar curve r= 6+2 sin(30)? %3D

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Q: area

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Q: Is the formula for area in polar coordinates valid if f (θ) takes negative values?

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Q: 5. Convert the integral 9-x2 9-x²-y² Vx? + y? + z² dzdydx to spherical coordinates then evaluate.

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Q: Find the length of the cardioid r = 1 + sinθ

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Q: Find the angle in radians between the planes -2x + z = 1 and -ly+ z = 1.

A: See the answer below

Q: 2) | cos(r + y)dA, R is the unit disk (i.e. the region inside the unit circle)

A: This double integral can be easily solved in polar coordinates. A brief introduction to polar…

Q: Evaluate the spherical coordinate integral. 7/2 7/3 8 sec 8 sec o Q sin o cos o do do de 5 sec o

A: We have to find the value of given integral.

Q: Use the parametric equations of an ellipse, x a cos(0), y = b sin(0), 0 seS 2n, to find the area…

A: Given that the parametric equation of an ellipse is  x= a cos(θ) , y=b sin(θ) , 0≤ θ ≤ 2π . Here we…