Question

Suppose r is the shaded region in the figure, and f(x, y) is a continuous function on r. Find the limits of integration for the iterated integral ∬r f(x, y) da = ∫ba ∫dc f(x, y) dy dx.

a) ∫dc ∫ba
b) ∫ba ∫dc
c) ∫dcb ∫ab
d) ∫bac ∫dcb

Answer 1

To find the limits of integration for the iterated integral ∬r f(x, y) da = ∫ba ∫dc f(x, y) dy dx, the limits of integration a and b correspond to the outer integral with respect to x, and the limits of integration c and d correspond to the inner integral with respect to y.

Step-by-step explanation:

To find the limits of integration for the iterated integral ∬r f(x, y) da = ∫ba ∫dc f(x, y) dy dx, we need to determine the order of integration. In this case, the limits of integration a and b correspond to the outer integral with respect to x, and the limits of integration c and d correspond to the inner integral with respect to y.

Therefore, the correct answer is Option a) ∫dc ∫ba.