The integral of exponential refers to the process of finding the area under the curve of an exponential function. It is denoted by ∫exdx and is equal to ex + C, where C is the constant of integration.
To solve an integral of exponential, you can use the power rule of integration, which states that ∫xndx = (xn+1)/(n+1) + C. In the case of an exponential function, you can rewrite it as ex = (e1)x and then apply the power rule to solve the integral.
The properties of integral of exponential include linearity, which means that the integral of a sum of two or more exponential functions is equal to the sum of their individual integrals. It also follows the power rule of integration and has a constant of integration, which can be determined by using initial conditions.
The integral of exponential is important because it is used in various fields of science, such as physics, engineering, and economics, to model exponential growth and decay. It can also be used to solve differential equations, which are fundamental in understanding natural phenomena.
The integral of exponential has many applications, including calculating compound interest in finance, determining population growth in biology, and analyzing radioactive decay in physics. It is also used in signal processing, probability and statistics, and many other areas of science and mathematics.