Two integrals refer to the mathematical concept of integrating a function over a given interval or region. It involves finding the area under a curve or the volume of a solid using a specific set of mathematical rules and techniques.
A definite integral has specific upper and lower limits of integration, while an indefinite integral does not have these limits and results in a general solution. In other words, a definite integral gives a specific numerical value, while an indefinite integral gives a function.
The fundamental theorem of calculus states that differentiation and integration are inverse operations. This means that if a function is integrated and then differentiated, the resulting function will be the same as the original function.
Integration has many real-life applications, such as calculating the area under a curve in physics and engineering, finding the volume of irregular-shaped objects in architecture, and determining the total cost of a production process in economics.
Some common techniques for solving integrals include substitution, integration by parts, trigonometric substitution, and partial fractions. These techniques involve using specific rules and formulas to simplify the integral and find the solution.