# What is #int_(0)^(1) e^(5x^2)dx #?

You'll need to use numerical methods for this, as the integrand does not have a nicely expressible antiderivative.

I suggest using the trapezoidal or Simpson's approximation.

Wolfram Alpha gives

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The integral of (e^{5x^2}) from (0) to (1) is approximately (0.511808) using numerical methods.

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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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