Unique Integral Calculus Course for Homeschoolers and Self-Learners

It is the value of functions found in the process of integration.  Basically, integration is the process of getting f(x) from f'(x) and integral calculus helps in finding integrals of the function. To find an integral is the inverse process to find a derivative. The integral of a function represents the family of the curve. We can say integral represents the area under the curve. In mathematical terms, an integral evaluates the area, volume, work, and displacement under the area of the curve.

Types of Integral

Integral is used for solving two types of problems; the first is to find the functions of its given derivatives and the second is to find the area bounded by the graph of the function under a given condition. As we know the use of integral and how it helps in solving problems, so types are:
Definite Integral: In a definite integral the value of the integral is definite.
Indefinite Integral: In indefinite integral the value of integral is indefinite.

Fundamental Theorem of Calculus

The basic principle of calculus relates derivatives to integrals and provides the principal method for evaluating. In short, it means any function that is continuous for a specific interval has an antiderivative for that interval. Particularly it shows the functional relationship between derivative and integral. The theorem is of two types.

●      First Fundamental Theorem of Calculus

The equation of first fundamental theorem of calculus is A(x) =  b∫ a f(x) d x for all x ≥ a, where a and b are under continuous function and A'(x) is equal to f(x) ϵ [a,b].

●      Second Fundamental Theorem of Calculus

In this f is continuous function of x in a closed interval ( a, b) and F will be indicated as another such function such as d /dx F (x) = f (x) this is for all the x is the domain of f; then b ∫ a f(x) dx = f(b) -f(a). We can also call this definite integral of f for the range of (a, b), in which a will be represented as the lower limit and b will be indicated as lower.

Difference Between Differential and Integral Calculus

Integral calculus deals with the theory and applications of integrals while the focus of differential is on the rate of change such as velocities and tangent lines. And calculus deals with size and value like length, volume, and areas. This is how both of them were different from each other but they were connected by the fundamental theorem of calculus. They were connected through this medium as it shows how a definite integral is calculated by using antiderivatives.

Integration by Parts

Through , we can find the integral of the product of functions in terms of integration of the product of their derivative and antiderivative. We can use it to transform the antiderivative of product function to antiderivative of solution which can be found more easily. The formula of integration by part is ∫u v dx = u∫v dx −∫u’ (∫v dx) dx  where u is the function u(x); v is also function v(x) and u represents the derivative of the function u (x). With the help of this formula hope you get the concept of integral by parts now we will learn more about integral calculus.

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