Examples of using Indefinite integral in English and their translations into Swedish
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Maybe, OK, so we have that indefinite integral.
It's an indefinite integral of-- dx is on the numerator, right?
We learned in the previous indefinite integral module, right?
so we just set up the indefinite integral.
We want to know our indefinite integral in terms of x.
And we're ready to substitute back into our original indefinite integral.
Let's say we want to take the indefinite integral of x cosine of x d of x.
So my indefinite integral becomes the square root of 3 over the square root of 2 cosine theta d theta, all of that over the square root of 3 times the cosine squared of theta.
Then I want to subtract the indefinite integral of f prime of x.
So my indefinite integral now becomes the integral,
This is essentially just-- this is the indefinite integral of x squared plus 1.
So our indefinite integral in terms of theta,
We have figured out the antiderivative, the indefinite integral of x squared e to the x is this big fancy thing.
But the actual indefinite integral says, well,
you could do it as one indefinite integral.
But in this case, the indefinite integral is just saying,
you probably realize, well the indefinite integral even though it looks like fancy math,
Let's say I have the indefinite integral 1 over the square root of 3 minus 2x squared.
well that just becomes-- and we're doing the indefinite integral, kind of the antiderivative,
Let's say we have the indefinite integral of 1 over 36 plus x squared d x.
We're learning the indefinite integral, but we could learn use the definite integral,
In this presentation I'm just going to do a bunch of examples of taking the antiderivative or the indefinite integral of polynomial expressions, and hopefully I will show you
If I wanted to take indefinite integral and you could do a web search for integral and you will see this drawn properly-- take the indefinite integral-- let me make a big expression.
I just algebraically rewrote this indefinite integral as this indefinite integral. They are equivalent.
it's really, all the indefinite integral, is is you can kind of view it as a sum, right?
we could just write the indefinite integral, and I'm not going to rewrite the fundamental theorem from calculus,
So our original indefinite integral, which was all of this silliness up here,
Let's say I want to take the indefinite integral of 3x to the -5- 7x to the third+ 3- x to the ninth.
Let's say we have the indefinite integral of the square root of 6x minus x squared minus 5.
Some authors define the indefinite integral of a function as the set of its infinitely many possible antiderivatives.