onvert the integral below to polar coordinates and evaluate the integral. instructions: please enter the integrand in the first answer box, typing theta for . depending on the order of integration you choose, enter dr and dtheta in either order into the second and third answer boxes with only one dr or dtheta in each box. then, enter the limits of integration and evaluate the integral to find the volume. a

In math, polar coordinates refer a pair of coordinates locating the position of a point in a plane, the first being the length of the straight line ( r ) connecting the point to the origin, and the second the angle ( θ ) made by this line with a fixed line.

Here we have the limits of integration and evaluate the integral to find the volume. for the polar coordinates.

Here we have the polar representation of a point P is the ordered pair (r,θ) where r is the distance from the origin to P and θ is the angle the ray through the origin and P makes with the positive x-axis.

Then the polar coordinates r and θ of a point (x,y) in rectangular coordinates satisfy

=> r=x² + x² and tan⁡(θ)=yx;

Here the rectangular coordinates x and y of a point (r,θ) in polar coordinates satisfy and x=rcos⁡(θ) and y=rsin⁡(θ).

Then the area element dA in polar coordinates is determined by the area of a slice of an annulus and is given by dA=rdrdθ.

Here we have to convert the double integral ∬Df(x,y)dA to an iterated integral in polar coordinates,

Now, we have to substitute rcos⁡(θ) for ,x, rsin⁡(θ) for ,y, and rdrdθ for dA to obtain the iterated integral

=> ∬Df(rcos⁡(θ),rsin⁡(θ))rdrdθ.

To know more about Polar coordinates here.

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