To sketch the area of integration of a double polar integral, you’ll need to analyze the function and evaluate both sets of limits separately. Remember, you’ll need to sketch the polar function on polar coordinate axes, where the r values represent the radius of a circle and the theta values will produce straight lines.
Read MoreYou can use a double integral to find the area inside a polar curve. Assuming the function itself and the limits of integration are already in polar form, you’ll be able to evaluate the iterated integral directly. Otherwise, if either the function and/or the limits of integration are in rectangular form, you’ll need to convert to polar before you evaluate.
Read MoreIf we’re given a double integral in rectangular coordinates and asked to evaluate it as a double polar integral, we’ll need to convert the function and the limits of integration from rectangular coordinates (x,y) to polar coordinates (r,theta), and then evaluate the integral. We can do this using the formulas to convert between rectangular and polar coordinates.
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