Examples of using The integral from in English and their translations into Polish
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So this becomes the integral from t is equal to o to t is equal to pi over 2-- I don't like this color--of cosine of t, sine of t, cosine times sine-- that's just the xy.
Your Dirac delta function is a function of t, and because of this, if you ask what's the limit as tau approaches zero of the integral from minus infinity to infinity of d sub tau of t dt, well,
So if we do the substitution on this crazy, hairy-looking interval, let's simplify a little bit, and it changes our-- so this integral is going to be the same thing as the integral from u, when t is a, u is b.
waking up is as easy as counting the integral from the exponential of a square.
So this is equal to sine of t times the integral from 0 to t of cosine squared of tau d tau and then minus cosine of t-- that's just a constant; I'm bringing it out-- times the integral from 0 to t of sine of tau cosine of tau d tau.
So we said is, well, to figure out the area of that we're just going to take the integral from t is equal to o to t is equal to pi over 2-- it doesn't make a lot of sense when I write it like this--of f of xy times-- or let me even better, instead of writing f of xy, let me just write the actual function.
ds is equal to the integral from t is equal to a,
And we can just use the definition of the Laplace transform, so this is equal to the area from 0 to infinity, or we could call it the integral from 0 to infinity of e to the minus-- that's just part of the Laplace transform definition-- times this thing-- and I will just write it in this order-- times f of t times our Dirac delta function.
That equals the negative of the integral from b to a of f of x dx.
Well, this is going to be equal to the integral from 0 to pi over 2 of x plus y squared.
And the actual area under the curve is denoted by the integral from a to b of f of x times dx.
let's say as A approaches infinity of the integral from 0 to Ae to the minus st. dt.
So we want to evaluate pi squared over 10 times the integral from -10 to 10 of f(x) cos(pi*x), using the logic we just talked about, this is going to be the same thing as being equal to pi squared over 10, pi squared over 10, times the integral, well, times the integral, of, from 0 to 1 but 20 times that.
And then we still have the outside integral from 0 to 2 dx.
This weighting distinguishes the line integral from simpler integrals defined on intervals.
So that's the improper integral from 0 to infinity of e to the minus st times 1 here.
The improper integral from 0 to infinity of e to the minus st times f of t-- so whatever's between the Laplace.
This is equal to the limit as n approaches negative infinity of the definite integral from n to 0 of 250 over 25 plus x squared dx.