Integral calculus is a branch of mathematics that deals with the calculation of areas, volumes, and other quantities that are related to a curve or a surface. It is essentially the inverse operation of differentiation and is used to find the accumulation or total change of a function over a given interval.
Integrals are important because they allow us to solve various real-world problems by finding the total change or accumulation of a quantity. They are used in various fields such as physics, economics, and engineering to model and analyze various systems.
To integrate a function, you need to first find the antiderivative of the given function. This can be done by using various integration techniques such as substitution, integration by parts, or trigonometric substitution. Once the antiderivative is found, the integral can be evaluated by plugging in the limits of integration and taking the difference.
A definite integral has specific limits of integration and gives a numerical value, while an indefinite integral does not have any limits and gives a general antiderivative function. In other words, a definite integral gives a specific answer, while an indefinite integral gives a family of possible answers.
To check if an integral is solved correctly, you can take the derivative of the antiderivative and see if it matches the original function. If it does, then the integral is solved correctly. You can also use online tools or calculators to verify your answer.