Compute the area of the finite region bounded by the graphs of the functions $y = 5 x ^ { 2 }$ ,and $y = - 5 x ^ { 2 } - 20 x + 80$ .
A)360
B)320
C)280
D)240

Question

Quizplus · Accepted Answer

The area between the curves is found by integrating the difference of the functions over the interval where they intersect. Solving $5x^2 = -5x^2 - 20x + 80$ gives intersection points at $x = -4$ and $x = 2$. Integrating the difference $(-5x^2 - 20x + 80) - (5x^2)$ from $-4$ to $2$ gives an area of 360.

Compute the Area of the Finite Region Bounded by the Graphs