Q.Sketch the region bounded by the graphs of: $\displaystyle y=9-x^2, y=5-3x$ and then find it's area.

A.$\displaystyle A = \int_{-1}^{4}(9-x^2)-3x dx = \left[-\frac{1}{6}x(x(2x+9)-54\right]_{-1}^{4}$

$\displaystyle = -\frac{1}{6}4(4(2*4+9)-54) - (-\frac{1}{6})-1(-1(2*(-1)+9)-54)$

$\displaystyle = -\frac{56}{6} - \left[-\frac{61}{6}\right] = -\frac{5}{6}$