Integral Calculus 1 - Ολοκληρωτικός Λογισμός 1

Uploaded by MrJohnchios on 10.06.2012

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In this video we will learn how a indefinite indegral could be calculated.
In calculus, an antiderivative, primitive integral or indefinite integral...
of a function f is a function F whose derivative is equal to f, i.e., F ? = f.
The process of solving for antiderivatives is called antidifferentiation...
...or indefinite integration and its opposite operation is called differentiation,
which is the process of finding a derivative.
To follow this chapter, is required to know how we find derivative.
Exercise 1
Find the antiderivative of the function f(x) = 3x^2.
We want to find function F whose derivative is the given function f.
One of these functions is: F(x) = x^3.
Because: F´(x) = (x^3) = 3x^2 = f(x).
Of course there are and others antiderivatives, like is F(x) = x^3 + 5.
Exercise 2
Prove that F(x) = xexp(x) – exp(x) is one of antiderivatives of the f(x) = xexp(x).
Definition of the indefinite integral.
The fundamental theorem of calculus is a theorem that links the concept…
…of the derivative of a function with the concept of the integral.
Please write the properties of the indefinite integrals.
Now, we see some of well-known indefinite integrals.
Please note these indefinite integrals.
The “óõíx” is the same with cos(x).
The “çìx” is the same with sin(x).
The “åöx” is the same with tan(x).
The “óöx” is the same with cot(x).
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