# How do you find the definite integral of #e^(x^2) dx# from #[2, 3]#?

# int_2^3 \ e^(x^2) \ dx ~~ 1428.092495127207 #

This cannot be computed using known elementary functions - It would require a numerical approximation. Using such a method we obtain:

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To find the definite integral of ( e^{x^2} ) from ( x = 2 ) to ( x = 3 ), you would typically need to use numerical methods as there isn't a standard antiderivative for ( e^{x^2} ). One common numerical method is the use of approximation techniques such as Simpson's rule or the trapezoidal rule. These methods approximate the integral by breaking the interval into smaller subintervals and approximating the function within each subinterval using simple shapes like trapezoids or quadratic curves. By summing up these approximations, you can estimate the value of the definite integral within the given interval.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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