And I would agree with you...tnutty said:Homework Statement
integral [from e to infinity of ] 67 / (x(ln(x))^3)
read as the integral from e to infinity of
67 divided by x times cubed lnx.
The Attempt at a Solution
i know it converges,
but i got the value
67/2
The integral from e to infinity is a mathematical concept that represents the area under a curve from the value of e to infinity. It is typically written as ∫e^x dx and is used in calculus to solve problems related to rates of change and accumulation.
The integral from e to infinity is usually calculated using integration by parts or substitution, as it involves solving an infinite limit. It can also be approximated using numerical methods, such as the trapezoidal rule or Simpson's rule.
The number e (approximately 2.718) is a special mathematical constant that appears frequently in natural and exponential growth. Using e in the integral from e to infinity allows us to solve problems related to exponential functions and continuously growing quantities.
The integral from e to infinity is an essential tool in calculus and mathematical analysis. It is used to solve various problems related to rates of change, growth, and accumulation, making it a fundamental concept in many areas of mathematics and science.
Yes, the integral from e to infinity has a wide range of real-world applications, such as in physics, engineering, and economics. For example, it can be used to calculate the total amount of heat generated over time, the population growth of a species, or the accumulated interest on a continuously compounding investment.