Examples of using The integral of in English and their translations into Swedish
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The integral of a dose profile D(z),
if we wanted to figure out, the,  the integral of the  product of these two periodic functions,
times the integral, of, from 0 to 1 but 20 times that.
So this, as we see, simplifies to the integral of u to the  minus 3 du,
you're left with, that this is equal to the integral of u to the  third du.
Now we can take the integral of both sides of  this equation,
So my indefinite integral  now becomes the integral,  I'm just doing a little bit of  algebra, the integral of the  square root of 4 minus x minus 3 squared dx.
Because we know that the integral of say x to the  fourth dx is equal to-- I mean x to the  third dx-- is equal to 1/4 x to the  fourth.
So my integral  becomes the integral of 2 times 1,
Sets the  initial x and y point for the integral of the  function with the ID id to x
So I get the integral of e to the  x cosine of  x d x is equal to e to the  x cosine of  x plus the integral of e to the  x sine of  x d x.
What if I had the integral of let's say-- this is actually one that's often kind of  viewed as a trick, but you will see it's actually not that tricky of  a trick.
I want to take the  integral-- and actually you can see kind of  how I'm thinking about these problems-- I'm going to take the integral of cosine of  x times the  sin of  x to the  third power dx.
we're essentially saying that we want to take the integral of something where we have the  derivative of  kind of the  inner function,
It's not systematic-- that's g prime of  x-- that equals f of  access times g of  x-- this is how it's the  product rule in reverse-- minus the integral of the  derivative of the  first function, f prime of  x, times the  second function.
minus, the integral,  minus the integral of v, which is 1/pi sin(pix)
you're taking the integral of a derivative, you just get back to what you took the  derivative originally of, so this just becomes f of  x times g of  x, and then we have to integrate the  right hand side, well that just becomes-- and we're doing the  indefinite integral, kind of the  antiderivative, but we can use this tool when we do definite integrals as well.
In the  branch of  mathematics known as real analysis, the  Riemann integral,  created by Bernhard Riemann, was the  first rigorous definition of the integral of  a function on an interval.
The integral part of the  order is a graphic design of the  product.