Consider the functions given by $f(x) = 5-(x-1)^2$ and $g(x) = 4-x$.

(a) Use algebra to find the points where the graphs of $f$ and $g$ intersect. (If more than one point, use a comma to separate them.)
Point(s):

(b) Use https://www.desmos.com/calculator to accurately graph the functions $f(x)$ and $g(x)$. Check to see if the points you found in part (a) are accurate.

(c) Find and evaluate exactly an integral expression, $\int_a^b h(x)\ dx$, that represents the area between $y = f(x)$ and the $x$-axis on the interval between the intersection points of $f$ and $g$.

$a$ =

$b$ =

$h(x)$ =

$\int_a^b h(x)\ dx$ =

(d) Find and evaluate exactly an integral expression, $\int_a^b h(x)\ dx$, that represents the area between $y = g(x)$ and the $x$-axis on the interval between the intersection points of $f$ and $g$.
$a$ =

$b$ =

$h(x)$ =

$\int_a^b h(x)\ dx$ =

(e) What is the exact area between $f$ and $g$ between their intersection points?

Answer: