# What is the arclength of #f(x)=x^5-x^4+x # in the interval #[0,1]#?

approximately

This can't be integrated by hand, so stick it into a calculator to see that

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To find the arc length of the function ( f(x) = x^5 - x^4 + x ) on the interval ([0, 1]), use the formula for arc length:

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

Where ( \frac{dy}{dx} ) represents the derivative of ( f(x) ).

First, find the derivative of ( f(x) ), then plug it into the formula along with the limits of integration and evaluate the integral to find the arc length.

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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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