Integration is a mathematical process of finding the area under a curve. It involves breaking down a shape into smaller, simpler shapes and adding up their areas to find the total area.
To find the concavity of a curve, you need to take the second derivative of the function and then analyze its sign. If the second derivative is positive, the curve is concave up. If it is negative, the curve is concave down. If it is zero, the curve has a point of inflection.
The purpose of integrating a curve is to find the area under the curve, which can be used in various real-world applications such as calculating volumes, distances, and probabilities.
There are several methods of integration, including the power rule, substitution, integration by parts, and trigonometric substitution. Each method is used for different types of functions and can be helpful in solving complex integration problems.
Definite integration involves finding the exact value of the area under a curve between two specific points. Indefinite integration, on the other hand, involves finding a general solution for the integral without specifying the limits of integration.