Find the area of the region bounded by the given curves. $y=x^{2}-6 x, y=5 x+12$
A) $2197$
B) $\frac{25}{3}$
C) $\frac{2197}{3}$
D) $\frac{2197}{6}$
E) 6

Question

Quizplus · Accepted Answer

To find the area between the curves, first find the points of intersection by setting $x^2 - 6x = 5x + 12$. Solving gives $x^2 - 11x - 12 = 0$, which factors to $(x-12)(x+1) = 0$, so $x = 12$ and $x = -1$. The area is the integral from $-1$ to $12$ of $(5x + 12) - (x^2 - 6x)$ dx, which simplifies to $-x^2 + 11x + 12$. Integrating and evaluating from $-1$ to $12$ gives $\frac{2197}{6}$.

Find the Area of the Region Bounded by the Given y=x2−6x,y=5x+12y=x^{2}-6 x, y=5 x+12y=x2−6x,y=5x+12

Find the Area of the Region Bounded by the Given $y=x^{2}-6 x, y=5 x+12$