Note: please write down the Answer by hand on paper and also write each answer with the number of the questions

7. Verify One of the following results. ( 2 ) 6 " 3 (x2 + y?) da dy = 35 -71 / 2 rsin 8 cos 0 3TT (b ) r sin2 0 cos2 0 dr d0 = Jo 5128. Evaluate One of each of the following integrals. (a) 1 xy ery dxdy (b) / JD xy dA, where D is the region bounded by the line y = x - 1 and the parabola 92 = 2x + 6.9. A surfboard company has developed the yearly profit equation P(x, y) = -22x2 + 22xy - lly + 110x -44y - 23, where x is the number (in thousands) of standard surfboards produced per year, y is the number (in thousands) of competition surfboards per year, and P is the profit (in thousands of dollars). How many of each type board should be produced per year to realize a maximum profit? What is the maximum profit