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

Answer 1

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

Although #inte^(5x^2)# can be written using the imaginary error function, #"erfi"#, to calculate it, requires numerical methods.

I suggest using the trapezoidal or Simpson's approximation.

Wolfram Alpha gives

#int_0^1 e^(5x^2) = 1/2sqrt(pi/5)"erfi"(sqrt5)~~ 17.1722#

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Answer 2

William Abdalla

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

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Answer from HIX Tutor

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.