Can't finish equation solving step :p area between functions

[franklingroye]

Homework Statement

The two functions are x² and mx, where m is a positive constant. I'm asked to find the value for m where the region enclosed between the two equations in the first quadrant is equal to 8.

Homework Equations

n/a

The Attempt at a Solution

Since m is a constant, x² and mx intersect at x = 0 and x = m. So therefore, the area between the equations would be:

($\frac{m}{2}$x² - $\frac{1}{3}$x³)|$^{m}_{0}$

Which simplifies to:

$\frac{m}{2}$m² - $\frac{1}{3}$m³

So clearly all I need to do is set it equal to 8 and solve... however, I'm having major issues actually accomplishing this. I can't see how to get it so I just have m = (constant). Can anyone help? I know the answer I'm trying to get is ~3.63424 but no clue how to get there.

 

[Oster]

m^3(1/2 - 1/3)=8
just get m^3 on one side by multiplying/dividing the equation by some appropriate number?

 

[franklingroye]

m^3(1/2 - 1/3)=8
just get m^3 on one side by multiplying/dividing the equation by some appropriate number?

My gosh, I didn't even notice that (m/2)(m^2) simplified to 1/2m^3. I feel so stupid now! Thank you :) I've been trying to solve it keeping the three different powers of m

 

[Oster]

no problem =)