An indefinite integral is the reverse process of differentiation. It represents a family of functions whose derivative is equal to the given function. It is denoted by the symbol ∫.
To evaluate an indefinite integral, you need to use integration techniques such as substitution, integration by parts, or partial fractions. You can also use tables of integrals or online calculators to obtain the result.
A definite integral has specific limits of integration and gives a numerical value, while an indefinite integral has no limits and represents a family of functions. A definite integral can be used to find the area under a curve, while an indefinite integral is used to find the original function.
Some common mistakes include forgetting to add the constant of integration, not applying the chain rule correctly, and not simplifying the integrand before integrating. It is also important to check for any errors in arithmetic or algebraic manipulation.
Indefinite integrals are used in various fields of science and engineering, such as physics, economics, and computer science. They can be used to model and analyze real-life situations, such as predicting the growth of a population or calculating the work done by a force.