If 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.
Read MoreWe already know that we can use double integrals to find the volume below a surface over some region R=[a,b]x[c,d]. We can define the region R as Type I, Type II, or a mix of both. Type I curves are curves that can be defined for y in terms of x and lie more or less “above and below” each other. On the other hand, Type II curves are curves that can be defined for x in terms of y and lie more or less “left and right” of each other.
Read MoreThe Theorem of Pappus tells us that the volume of a three-dimensional solid object that’s created by rotating a two-dimensional shape around an axis is given by V=Ad. V is the volume of the three-dimensional object, A is the area of the two-dimensional figure being revolved, and d is the distance traveled by the centroid of the two-dimensional figure.
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