Final answer:
To evaluate the double integral, convert it to polar coordinates and simplify the expression. Evaluating the integral gives the result.
Step-by-step explanation:
To evaluate the double integral ∫∫(D) (5x - 9y) dA, we need to determine the region D bounded by the circle with center at the origin and radius 1.
Since D is a circle, we can express it in polar coordinates. The equation of the circle can be written as r = 1, where r is the radial distance from the origin.
Converting the double integral to polar coordinates, we have:
∫∫(D) (5x - 9y) dA = ∫∫(D) (5rcos(θ) - 9rsin(θ)) r dr dθ
Simplifying the integral and evaluating, we get:
∫∫(D) (5x - 9y) dA = ∫(θ=0 to 2π) ∫(r=0 to 1) (5rcos(θ) - 9rsin(θ)) r dr dθ