Evaluate the antiderivative as a Taylor Series

brojas7
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Homework Statement



Evaluate the anti derivative ∫e^x^2 dx as a Taylor Series

Homework Equations



\frac{f^(n)(a)}{n!}(x-a)^n

The Attempt at a Solution


Where do I start, I am not sure I understand the question
 
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brojas7 said:

Homework Statement



Evaluate the anti derivative ∫e^x^2 dx as a Taylor Series

Homework Equations



\frac{f^{(n)}(a)}{n!}(x-a)^n

The Attempt at a Solution


Where do I start, I am not sure I understand the question
You need to include an attempt at solving the problem, before anyone can help you.

What is the Taylor series for ex ?
 
brojas7 said:

Homework Statement



Evaluate the anti derivative ∫e^x^2 dx as a Taylor Series

Homework Equations



\frac{f^(n)(a)}{n!}(x-a)^n

The Attempt at a Solution


Where do I start, I am not sure I understand the question

What is the integrand? Is e^x^2 supposed to be ##(e^x)^2##, or is it ##e^{x^2}?## If you mean the first one, what you have written is correct (but it would still be better to use parentheses and write (e^x)^2); if you mean the second one it is essential to use parentheses, like this: e^(x^2).
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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