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arslan894
- 9
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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
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.
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.
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.
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.
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.