Hey casanova, welcome to PF!casanova2528 said:can anybody help me with this integration?
Integral of e to the -2x times x squared dx
it expands to 1/4, but I'm not sure how to start.
casanova2528 said:with what do I start?
Integration is a mathematical technique used to find the area under a curve. It is important because it allows us to solve real-world problems involving rates of change, distance, and many other physical quantities.
Definite integration involves finding the exact numerical value of the area under a curve between two specified points. Indefinite integration, on the other hand, involves finding a general formula for the integral that can be used to find the value of the area at any point.
The Taylor expansion is a mathematical series that represents a function as an infinite sum of terms. It can be used to approximate the value of a function at a given point, which is helpful in integration as it allows us to solve integrals that cannot be solved using traditional methods.
Yes, there are limitations. The Taylor expansion only provides an approximation of the function, so the more terms we include, the more accurate the approximation becomes. However, if we include too many terms, the calculation can become too complex and time-consuming.
Yes, integration and Taylor expansion have many applications in physics, engineering, economics, and other scientific fields. They can be used to solve problems involving rates of change, optimization, and many other real-world problems.