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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???

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.

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?

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.

Re: find the area of the region bounded by the graphs of the equations.

Re: find the area of the region bounded by the graphs of the equations.

Take the integral bounded at the intersection points.

Re: find the area of the region bounded by the graphs of the equations.

$\displaystyle y = 0$ is the x-axis

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

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

$\displaystyle x(3-x) = 0$

... the zeros, $\displaystyle x = 0$ and $\displaystyle x = 3$ are the limits of integration.

Re: find the area of the region bounded by the graphs of the equations.

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?

Re: find the area of the region bounded by the graphs of the equations.

$\displaystyle \int\limits_a^b f(x) dx = F(b)-F(a) $