Integral Calculus Reviewer By Ricardo Asin Pdf 54 Online

So bracket = (\frac27\pi4 + 9).

Therefore: [ W = 196000 \left( \frac27\pi4 + 9 \right) \quad \textJoules. ] 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. So bracket = (\frac27\pi4 + 9)