/sci/ - Science & Math

[Anonymous No.3713575]

Hello! I sometimes see things like this:
<div class="math">\int_{~}^{x}f(t)~dt</div>
What does it mean to integrate with another variable as an upper bound, and why does it work?

[Krakengineer !!5XY+x7grkpt No.3713580]

Just replace all the t's with x's after you're done.

[Anonymous No.3713581]

it just means an indefinite integral.

if you put the k as a lower bound you would get F(x) - F(k) = F(x) + c

[Anonymous No.3713582]

>>3713575
pic related

[Anonymous No.3713584]

there has to be a lower bound too, and then it can be visualized as a new function of x, where the value of x is the area under the curve f up to that point x.

[Anonymous No.3713586]

>where the value of x
I mean "where the value of this new function of x"

[Anonymous No.3713591]

>>3713584
>>3713581
Thank you. What is the utility of this as opposed to just replacing with x before integrating?

[Anonymous No.3713599]

i really fucking love that picture.

can't say i know anyone who has ever done that though.

[Krakengineer !!5XY+x7grkpt No.3713619]

>>3713591
Sometimes the equation has more than one variable, even more than one integral. Professors will even stick another equation under an integral where the x is if they're feeling hot.

It gets useful later on.

[Anonymous No.3713628]

>>3713591
it's just a function which summarizes alot of integrals. for example

int_0^1 f(x) dx

is some value, and

int_{-1}^8 f(x) dx

is some other value.

if you white

g(xstart,xend):=int_xstart^xend f(x) dx

then these two values are g(0,1) and g(-1,8).