Find the area of the plane z = 4x + 3y for all (r, y) E R where R is the region in the first quadrant which is bounded by the circle r = 10 sin (0) and V50 cos (20) both given in polar coordinates. Give your the lemniscate r = answer to the nearest four decimal places. A(S) = || () 1+ + dA, %3D ду R where R is the domain over which we are interested to find the area of the surface z. Sketch the region R before doing the integration. (In polar coordinates, dA = rdrd0)

Q: tegral by transforming to polar coordinates.

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

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Q: Determine the area in the first quadrant bound by the polar function r(0) = sin (0) – 1.

A: Here, since the area is in the first quadrant, we can calculate the area with the help of integral…

Q: Identify the correct plot that describes the polar region R-{(r, e )| 2 srs 5, n/2 s 0 s 3n/2}. -3-2…

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Q: + i5: and B = 4

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Q: Choose True if the statement is correct, otherwise False. The point (-13,–1107/4) is located between…

A: To convert the polar coordinates to the rectangular coordinates the formula used are x=rcos(θ),…

Q: r = 5 +4 cos 0 3. Draw and determine the area bounded by the curve in polar coordinates

A: We have to find the area bounded by the polar curve r = 5 + 4cos(theta)..

Q: Q4) Find plane area inside polar function r = 2 and outside polar function r = -2sine in third…

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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: Q5: Find the area of region enclosed by the polar function r= 3+3 sin 0

A: Plot

Q: D15 UT Determine the range for r and then the range for 8. Ob с -1 -2- Od -1

A: Given query is to find the correct graph:

Q: l+vI+r² xy dydx -z 1-VT-

A: ∫01∫1-1-x21+1+x2xydydxTo transform to polar coordinates and calculate