Integral f(x): -b to b, b=3

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In summary, the conversation revolves around finding the integral of the function f(x) = ∫e^(1-(x^2)/(b^2))dx with limits -b to b, where b = 3. The conversation discusses different methods of solving the integral, including substitution and numerical integration using the Simpson 3/8 rule. The conversation also mentions that the integral cannot be expressed in terms of standard functions, and provides a link to a Wolfram Alpha calculation of the integral. There is also a question about integrating a different function in MATLAB, which is not directly related to the original integral.
  • #1
arslan894
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f(x) = ∫e^(1-(x^2)/(b^2))dx the limits are -b to b , take the value of b = 3
 
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  • #2
Is this the integral?
[tex]
\int_{-3}^{3}e^\frac{1-x^2}{9}dx
[/tex]
 
  • #3
We're not going to do it for you. What have you tried?
 
  • #4
bro i tried it using substitution but the problem is that i can't go much further, @ DivisionByZro exp(1-(x^2/9))^.5
 
  • #5
Is this it?
[tex]
\int_{-3}^{3}e^\sqrt{1-\frac{x^2}{9}}dx
[/tex]
 
  • #6
yes bro
 
  • #7
Well, in any case, you won't find any substitutions since you don't have any "x" term multiplying the expression, therefore whatever you have in the exponent part can't be reduced. In other words, it wouldn't be as hard if your integral was something like:

[tex]
\int_{-3}^{3}xe^{x^{2}}dx
[/tex]

In this case if you let u=x2, then du=2xdx, and you could use substitution.

In fact there is no answer in terms of standard functions. What class/context was this for?
 
  • #8
i was modeling in MATLAB to find the friction between cam follower of an engine ,i used int function in MATLAB but it gave warning that explicit answer doesn't exist ,i used the simpson 38 rule to find the solution on paper but don't know how to use simpson 38 rule in matlab.
 
  • #9
any one knows how to do this function using simpson 3 8 rule in MATLAB ?
 
  • #11
I also have a doubt . Anybody reply fast


How to integrate

exp(x)*erfc(x) in MATLAB
 

1. What is an "Integral f(x): -b to b"?

An integral is a mathematical concept that represents the area under a curve. The notation "f(x): -b to b" indicates that we are calculating the integral of the function f(x) over the interval from -b to b.

2. What does the value of b represent in "Integral f(x): -b to b"?

The value of b indicates the upper and lower limits of the interval over which the integral is being calculated. In this case, the interval is from -b to b, meaning that the integral will be calculated over the entire range of x-values between -b and b.

3. How is the integral of a function calculated?

The integral of a function is calculated using a mathematical process called integration. This involves finding the antiderivative of the function and evaluating it at the upper and lower limits of the interval. The difference between these two values is the value of the integral.

4. What is the significance of the integral in mathematics?

The integral has many important applications in mathematics, including calculating areas, volumes, and other quantities. It is also used in physics, engineering, and other fields to model and analyze real-world situations.

5. Can the integral of a function be negative?

Yes, the integral of a function can be negative if the function has negative values over the given interval. This indicates that the area under the curve is below the x-axis. However, the integral can also be positive if the function has positive values over the interval, indicating that the area under the curve is above the x-axis.

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