# What is the arc length of #f(x) = x^2e^(3x) # on #x in [ 1,3] #?

This definite integral does not have an intrinsic solution and would need to be solved numerically, using either a computer or estimated using the Trapezium Rule or Simpson's Rule

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To find the arc length of (f(x) = x^2e^{3x}) on the interval ([1, 3]), we use the arc length formula:

[L = \int_{a}^{b} \sqrt{1 + \left(f'(x)\right)^2} , dx]

Where:

- (a) and (b) are the lower and upper bounds of the interval,
- (f'(x)) is the derivative of (f(x)).

First, find (f'(x)), then plug it into the arc length formula and integrate over the interval ([1, 3]).

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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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