Question

find the area of the region bounded by the functions f(x)=-x^2 +9x-4, x=-1, x=2, and y=0

Answer 1

x=-1. are you sure it isn't x=1?

Answer 2

yes im sure it is x=-1

Answer 3

i don't think there can be an area if y=0

Answer 4

that is why was not sure. so the answer is no area?

Answer 5

maybe, if you were not given that value however, you would integrate with the x values acting as limits.

Answer 6

thank you

Answer 7

\[\begin{align*}f(x)&=-x^2+9x-4\\\\
&=-\left(x^2-9x\right)-4\\\\
&=-\left(x^2-9x+\frac{81}{4}-\frac{81}{4}\right)-4\\\\
&=-\left(\left(x-\frac{9}{2}\right)^2-\frac{81}{4}\right)-4\\\\
&=-\left(x-\frac{9}{2}\right)^2+\frac{81}{4}-4\\\\
&=-\left(x-\frac{9}{2}\right)^2+\frac{65}{4}
\end{align*}\]

There's definitely an area...