Question 404203
For polar coordinates, the area would be given by the integral

{{{(1/2)int(r^2, d(theta), 0, pi)
=(1/2)int(4a^2cos^2(theta), d(theta), 0, pi)

= 2a^2int(cos^2(theta), d(theta), 0, pi)

}}}
={{{a^2int((cos(2theta) + 1), d(theta), 0, pi)}}}
={{{a^2(sin(2theta)/2 + theta)[0]^(pi))}}}
= {{{a^2(sin(2pi)/2 + pi - sin0/2 - 0)}}}
= {{{a^2pi}}}

NOTE: The polar equation is equivalent to the circle {{{(x - a)^2 + y^2 = a^2}}}, after changing to rectangular coordinates.
A direct calculation of the area of this circle using the formula {{{A = pi*r^2}}}
would give the same answer {{{a^2pi}}}.