How do you find the area of the region bounded by the polar curve #r=2+cos(2theta)# ?
The area inside a polar curve is approximately the sum of lots of skinny wedges that start at the origin and go out to the curve, as long as there are no self-intersections for your polar curve.
Each wedge or slice or sector is like a triangle with height
So add them up as an integral going around from θ=0 to θ=2π, and using a double angle formula, we get:
Now do the integral(s) by subbing u = 2θ and then u = 4θ, and remember to change limits for the "new u." I'll let you evaluate those to get practice integrating! Remember our motto,
"Struggling a bit makes you stronger." \dansmath/