Evaluate the following integral 6x + SS (8x - y) In (8x - y) dA R where R is the region bounded by the graphs of y = 8x - e6, y = 8x - e³, y = −6x + 3, and y = −6x + 2. Use the change of variables u = 8x - y, v = 6x + y.

Houriyya does a weekly exercise program consisting of cardiovascular work and weight training. Each week, she exercises for at least 10 hours. She spends at most 7 hours on weight training. She spends at most 12 hours doing cardiovascular work. Let x denote the time (in hours) that Houriyya spends doing cardiovascular work. Let y denote the time (in hours) that she spends on weight training. Shade the region corresponding to all values of x and y that satisfy these requirements.

-2- 3.) Find the area of the region bounded by the graphs of y = x² + x and y = 2x + 2.