this is not a homework question, I'm just curious.
Lets say there is a definite integral from 0 to x of a function (t^3 - 2t + 3)dt
If that function is set equal to a constant, how does one go about solving for x?
>>7689202
Evaluate the integral you fucking nigger
>>7689202
You mean how does one go about solving for t? If the function equals a constant, there's no need to have an integral at all. If the integral is equal to a known constant, you evaluate the integral and solve for t.
>>7689271
>>7689202
Integrate the cubic, get a quartic. In theory, you can solve a quartic algebraically, but it will be painful in general.
>>7689278
i dont mean solve for t, i mean solve for x
Literally just evaluate the integral and set it equal to a constant. Are you retarded?
>>7689290
Oh well I see. What person number 1 said.
To use an example, the integral of (1-x)dx from 0 to t, = 3
So, int(1-x)dx = 3
x-0.5x^2 (from 0 to t) = 3
t-0.5t^2-0+0.5*0^2 = 3
t-0.5t^2 = 3
t(1-0.5t) = 3
t = 3
OR
1-0.5t = 3
-0.5t = 2
t = -4
Easy peasy.
I almost have x in terms of c but I don't know where to go from here.
Not OP btw
>>7689325
>the integral of 3dx is 3x^2/2
W-what?
Anyway, aside from that mistake you're almost there. From your last step (when it's corrected), plug in the limits of integration and solve algebraically. Factoring x^2 out of both terms will probably help.
Literally fucking integrate it.
x^4/4-x^2=constant
Solve for x
>>7689340
so...wait, what?
If the function is equal to a constant, you have to integrate both sides along that interval, right?
So it'd be
x^4/4-x^2= Constant*x
>>7689352
+ a constant
Kek. This board is retarded
>>7689360
Only if it's an indefinite integral.
It isn't though. It's from 0 to x.
>>7689202
integrate first, then solve for F(x) = c
F(x)-c = 0
i dont get what your question is, this should be simple.
LOL tardnigs
int 0 to x
(t^3 - 2t + 3) dt = 4
please prove this board is worthy
>>7689373
The answer is 4. The proof of this is trivial and left to the reader.
>>7689373
int 0 to x
(t^3 - 2t + 3) dt = 4
solve for x
>>7689318
>t(1-.5t)=3
>t=3
>OR
>t=-4
you can't do that unless the RHS is set equal to 0. plug in 3 and -4 into the original equation, neither of them work. I'm amazed that you're able to solve an integral with such a lack of algebraic knowledge, nevertheless you should leave this board forever.
>>7689282
type
solve 1/4 x (12-4 x+x^3) = C for x
into Wolfram alpha. It's a mess, but it can be done.
You guys are silly.
