Integrals with Common Fractions and Area Under Graph

[Brokenhope`]

I'm working on simple game and am working on a leveling system, using a function to get experience needed. I am using area under a function above y=0.

The first problem, I can't figure out a simple number.

f(x) = x²/5 dx

Then, looking for area, I'm unsure about a really simple thing.

Getting to x³/(3/5)

The last fraction I cannot figure out. Does the 5 move to the top and the 3 bottom?

I know how to calculate the area under the graph (for the leveling system,) but can I reverse engineer to be able to get the x-value on the graph from a given area.

Thanks.

 

[pwsnafu]

The antiderivative of $\frac{x^2}{5}$ is $\frac{x^3}{3 \times 5} = \frac{x^3}{15}$.

 

[Brokenhope`]

Thanks, that helped jog my memory.

The other thing I was hoping for finding a solution to.

I'm working on a Flash game and need a level system. Using a function and finding the filled area seems the best way.

The image kind of shows what I am trying to find.

Again, Thanks.

 

[chiro]

Hey BrokenHope.

If your area is analytic then you can just calculate the derivative of that function or better yet, calculate an inverse function that takes a y value and spits out an x value.

The inverse function is the better way especially if your function is not "analytic" and has all kinds of corners and jagged edges.

If the area function always rises for an increasing level of x, then you will always have an inverse function for all values of x.

 

[Brokenhope`]

Thanks for the response, chiro. I actually drew the graph wrong, and I am still a bit confused.

I have a new image of what I am trying to do.

Any help is greatly appreciated.

 

[pwsnafu]

You can always check if you got the right answer by using Wolfram|Alpha.

I'm trying to understand how you set up the problem. So $f(x) = 2\sqrt{x}$, okay sure. But say x=2 we get $2\sqrt{2} \sim 2.8$. What does that number mean?

 

[Brokenhope`]

I would round that value down to 2, for the "level." As for the experience needed, it would be shaded area from x = 0 to x = 2.

Thanks, hope that makes a bit more sense.

 

[pwsnafu]

I would round that value down to 2, for the "level."

Wait a sec. We have f(2) = 2 as the character's level yes. Does the x (not the shaded area), represent the character's current experience score?

As for the experience needed, it would be shaded area from x = 0 to x = 2.

You need to be specific. The experience needed to get from Level 0 to Level 2? Or the experience to get from Level 1 to Level 2?

 

[Brokenhope`]

Thanks for the replies.

I am actually only using the shaded area on the graph.

The shaded area to get to level 2, is the shaded area 0 to 2.

The shaded area is really just a running total of experience. To get to the next level, 3, your experience would be the area shaded from 0 to 3.

 

[chiro]

What is the formula for getting experience y given some level x?

 

[Brokenhope`]

This should make more sense.

But as a formula for experience/ leveling system, it's really kind of bad... the shaded area represents the experience.

Thanks.