Problem - evaluate intintd xy da where d is the region

Question

Problem - Evaluate ∫∫_D xy dA where D is the region bounded by y = x -1 and y2 = 2x +6 by the following the steps.

a) Find the intersection points of y = x -1 and y2 = 2x + 6.  

y = √2v+b                            y = x - 1

b. Graphically, what does y² = 2x + 6 look like? Where is the vertex of the graph of y² = 2x + 6?

c. Rewrite the functions in the form y = function of x. You should have three functions.

d. Rewrite the functions in the form x = function of y.

e. Graph the region D. In the picture, label your curves with the correct functions In terms of x. Draw vertical line segments, as though you were going to integrate with respect to y first.

f. Graph the region D again (use the grid above). In the picture, label your curves with the correct functions in terms of y. Draw horizontal line segments, as though you were going to Integrate with respect to x first.

g. Setup the integral integrating with respect to y first. Note: YOU ANSWER SHOULD SE A SUM OF TWO INTEGRALS!

h. Setup the integral integrating with respect to x first.

i. Compute the value of the integral.