Nicole18 said:the problem says y=f(x) and find the value of negative to positive infinityf(x)dx if it converges
f(x)={2-e^-.2x
{0
x is greater than or equal to 0
otherwise
...help
Nicole18 said:the problem says y=f(x) and find the value of negative to positive infinityf(x)dx if it converges
f(x)={2-e^-.2x
{0
x is greater than or equal to 0
otherwise
...help
Nicole18 said:yes the way chisigma wrote it is correct...i really have no idea how to even start this i need a precise answer. how do i tell if it converges i know converges means it is getting close to a number
The integral diverges since the exponential term goes to \(0\) as \(x\) becomes large, so the right tail of the integral is like the integral of a non zero constant (and of course the left tail converges since the integrand is zero for \(x\lt 0\).Nicole18 said:the problem says \(y=f(x)\) and find the value of \(\int_{-\infty}^{\infty}f(x)dx\) if it converges
\[f(x)=\begin{cases}2-e^{-0.2x}&\text{ for } x \ge 0\\0&\text{
otherwise} \end{cases}\]...help
The integral \(\int_{-\infty}^{\infty} f(x) dx\) for \(y=f(x)\) represents the area under the curve of the function \(f(x)\) from negative infinity to positive infinity. It is a way to measure the total value or total change of a function over a certain interval.
Finding the value of \(\int_{-\infty}^{\infty} f(x) dx\) for a specific function \(f(x)\) means calculating the numerical value of the integral, which represents the total area under the curve of the function from negative infinity to positive infinity. This value can be used to analyze the behavior of the function or to solve certain problems in mathematics and physics.
There are several methods for finding the value of \(\int_{-\infty}^{\infty} f(x) dx\) for \(y=f(x)\), such as the Fundamental Theorem of Calculus, integration by parts, substitution, and partial fractions. The choice of method depends on the complexity of the function and the problem at hand.
Finding the value of \(\int_{-\infty}^{\infty} f(x) dx\) for \(y=f(x)\) has various applications in mathematics, physics, and engineering. It can be used to calculate the area under a curve, the volume of a solid, the work done by a force, the probability of an event, and many other quantities in real-life situations.
Some common mistakes to avoid when finding the value of \(\int_{-\infty}^{\infty} f(x) dx\) for \(y=f(x)\) include forgetting to include the limits of integration, making algebraic errors while evaluating the integral, and not simplifying the result to its simplest form. It is important to carefully follow the steps of the chosen method and to check the final answer for accuracy.