Rico told the foreman, “About 5.9 megajoules.” The foreman nodded, and the pump worked perfectly—thanks to a slice, a distance, and an integral from page 54 of Ricardo Asin’s reviewer.
[ W = 196000 \int_-3^0 (3 - y)\sqrt9-y^2 , dy. ] Integral Calculus Reviewer By Ricardo Asin Pdf 54
Second integral: Let (u = 9-y^2), (du = -2y,dy), so (y,dy = -\frac12du). [ \int_-3^0 y\sqrt9-y^2,dy = \int_y=-3^0 \sqrtu \left(-\frac12 du\right) = -\frac12 \int_u=0^9 u^1/2 du = -\frac12 \cdot \frac23 u^3/2 \Big| 0^9 = -\frac13 (27) = -9. ] But careful with limits: actually (y=-3 \to u=0), (y=0 \to u=9), so (\int 0^9 \sqrtu (-\frac12 du) = -\frac12 \cdot \frac23 [27-0] = -9). Yes. Rico told the foreman, “About 5