OK, I''ve looked through my Calculus book and my notes from class, and for some reason I cannot find out how to do this! How do you integrate a constant? Like this: |-5 | 10 dx _| 0 (I dunno if that looks right, but I guess yall know what I mean.) Is it 50? 1? 0?

the constant can be taken out ie

Integral(a)dx
=
aIntegral()dx

which turns out to be
ax + c

is this what you are asking?

Think of it this way: the integral is the area under the curve y = 10 from x = -5 to x = 0. I''m sure you can find the answer yourself.

Cédric

But what about a definite integral?

Would it be 50 (in my previous example) since its like this:

10(5 - 0)

cause of the Fundamental Theorem of Calculus or whatever its called (if i''m even thinking of the right theorem, I just don''t know!)

oh i see (previous anon) what that was :>

yes... it would come out to be

10x

between 5 and 0

which indeed is

10(5-0) = 50

Brad: you may or may not know this, but please remember in the future that we like to keep a focus on gamedev-only math and physics.


Now to the problem.

/
| k dx
/

where k is a constant

is kx + c.

That means you have a trapeziod; and when you have that, you can find the area easily.

For a more calculus-based operation, examine the fundamental theorem of calculus like so:

f(x) = k

/b
| f(x) dx
/a

F(x) = kx + C

F(b) - F(a) = (kb + C) - (ka + C)

Which yields

kb - ka

Limits of integration are [b,a] aka [-5,0]
k = 10

Pushed into the equation:
= 10*-5 - 10*0

= 10(-5 - 0)

= 10*-5

= -50

Thats the definate integral from -5 to 0 of f(x).

Now I can`t rightly remember if you would set it up differenly for a area or simply take the absolute value.
Regardless, the area under that curve is 50 units.

~V''lion


Bugle4d

I''m sure you remember the "imaginary one" rule from Algebra - everything is being multiplied by an invisible one that you don''t write out because it''s assumed. Same concept when integrating a constant. However, this time you have an invisible variable, x⁰. You don''t write x⁰ because it equals one, but it still exists. So in your case, you really have this:
10x0dx
You can then apply basic anti-deriviation rules.

quote:

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10x0dx

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I never learned it that way, but it does make sense.

~CGameProgrammer( );

quote:

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Original post by Zipster
I''m sure you remember the "imaginary one" rule from Algebra - everything is being multiplied by an invisible one that you don''t write out because it''s assumed.

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Muuaahh....

More or less. 10 * x ^ 0 != 10, because 0 ^ 0 is not defined.

Cédric

quote:

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Original post by cedricl
Muuaahh....

More or less. 10 * x ^ 0 != 10, because 0 ^ 0 is not defined.

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I believe he was saying that x = 1, not x = 0. 1 ^ 1 = 1.