Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 4 16-y? (* +y) dx dy
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- Find the area of the region within the polar curve r1 = 9 cos θ but outside the polar curve r2 =3+3cosθ.Q 3/ find the area of circle of radius r, using double integral in polar coordinate P eI 1)Find the area enclosed by the loop of this polar curve: r=4costheta-2sectheta from -pi/3 to pi/3 using the formula A= 1/2 integral from -pi/3 to pi/3 (r)^2 dtheta.
- Consider a curve represented by x2 + y2 = 4x.(a) Find the polar equation of f.(b) Set up the integral to find the area inside the curve f and outside r = 2.Graph (either by hand or desmos) the polar curves r = 2 andr = 4 − 4 sin θ. Use a double integral to find the area inside thecircle, but outside of the cardioid.Find the area of the polar region f(θ)=4eθ/2f(θ)=4eθ/2 for 0≤θ≤3/2π0≤θ≤3/2π.
- 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)4piFind the surface area of the solid formed when r=4sin(theta) is revolved about the initial ray, thrta = 0.Evaluate the following by changing to polar coordinates. 3 ∫ 0 √ 49 − y2 ∫ √ 9 − y2 1 7 + x2 + y2 dx dy + 7 ∫ 3 √ 49 − y2 ∫ 0 1 7 + x2 + y2 dx dy