# find the area of the region bounded by the graphs of the equations.

• Dec 14th 2012, 04:13 PM
asilvester635
find the area of the region bounded by the graphs of the equations.
i know how the function looks like when graphed because i used a graphing calculator... but what does y=0 mean???
• Dec 14th 2012, 04:25 PM
chiro
Re: find the area of the region bounded by the graphs of the equations.
Hey asilvester635.

Setting y = 0 means that you are finding the solutions of when the function crosses the x-axis.

This is also known as finding the roots of the equation where f(x) = -x^2 + 3x = 0.

Finding roots to equations has many purposes.
• Dec 14th 2012, 04:33 PM
asilvester635
Re: find the area of the region bounded by the graphs of the equations.
how do i solve this??? like how do i find the area?? how do i go about solving this equation?
• Dec 14th 2012, 04:43 PM
chiro
Re: find the area of the region bounded by the graphs of the equations.
Start by factorizing the equation into (x-a)(x-b) = 0 and then use the fact that x = a and x = b are solutions to this equation since at least one term has to be 0 in order for the LHS to be zero.
• Dec 14th 2012, 05:00 PM
asilvester635
Re: find the area of the region bounded by the graphs of the equations.
i don't get it....
• Dec 14th 2012, 05:10 PM
Bean
Re: find the area of the region bounded by the graphs of the equations.
Take the integral bounded at the intersection points.
• Dec 14th 2012, 05:13 PM
skeeter
Re: find the area of the region bounded by the graphs of the equations.
$y = 0$ is the x-axis

so, you're looking for the area between the curve $y = 3x-x^2$ and the x-axis

note the curve intersects the x-axis when $3x-x^2 = 0$

$x(3-x) = 0$

... the zeros, $x = 0$ and $x = 3$ are the limits of integration.
• Dec 14th 2012, 05:50 PM
asilvester635
Re: find the area of the region bounded by the graphs of the equations.
thank you so MUCH!!!!!
• Dec 14th 2012, 06:02 PM
asilvester635
Re: find the area of the region bounded by the graphs of the equations.
so do i just straight up integrate the function? and then plug in the 3 and 0 into x?
• Dec 14th 2012, 06:58 PM
Bean
Re: find the area of the region bounded by the graphs of the equations.
$\int\limits_a^b f(x) dx = F(b)-F(a)$