Final answer:
To find the area enclosed by the curve r = 6 + sin(4theta), we can use the formula for finding the area of a polar region.
Step-by-step explanation:
To find the area enclosed by the curve r = 6 + sin(4θ), we can use the formula for finding the area of a polar region. The formula is A = ½∫[a, b] (r)^2 dθ. In this case, the curve is symmetric about the pole, so we only need to find the area in one quadrant and multiply it by 4. The limits of integration will be 0 to π/8.
Substituting the given equation r = 6 + sin(4θ) into the formula and evaluating the integral will give us the area enclosed by the curve.