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

The area is found by integrating the difference of the functions over the interval where they intersect. Solving $x^2 - 6x = 5x + 12$ gives intersection points at $x = -3$ and $x = 4$. The integral of $(5x + 12) - (x^2 - 6x)$ from $-3$ to $4$ results in $\frac{2197}{6}$.

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 $y = x ^ { 2 } - 6 x , y = 5 x + 12$