To change an iterated integral to polar coordinates we’ll need to convert the function itself, the limits of integration, and the differential. To change the function and limits of integration from rectangular coordinates to polar coordinates, we’ll use the conversion formulas x=rcos(theta), y=rsin(theta), and r^2=x^2+y^2. Remember also that when you convert dA or dy dx to polar coordinates, it converts as dA=dy dx=r dr dtheta.
Read MoreTo 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 MoreIterated integrals are double or triple integrals whose limits of integration are already specified. In this lesson, we’ll look at how to evaluate triple iterated integrals by working from the inside toward the outside.
Read MoreThere are six ways to express an iterated triple integral. While the function inside the integral always stays the same, the order of integration will change, and the limits of integration will change to match the order.
Read MoreWhenever we’re given a double integral, we want to turn it into an iterated integral, because with iterated integrals, we can easily evaluate one integral at a time, like we would in single variable calculus. When we evaluate iterated integrals, we always work from the inside out.
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