A circle of radius centered at the origin can be described either by in rectangular…
MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions
Problem
A circle of radius 5 centered at the origin can be described either by x2+y2=25 in rectangular form or by r=5 in polar form. Which statement best explains why evaluating the double integral for its area in polar coordinates is usually preferred?
(a) Polar coordinates automatically restrict the integration to the first quadrant only, reducing the work by a factor of four.
(b) Rectangular coordinates cannot represent circular regions without piecewise limits.
(c) The integrand becomes a constant, making the integral simpler to evaluate.
(d) Changing to polar eliminates the need to square the radius in the area formula.