# What is the arclength of #f(x)=x^2e^(1/x)# on #x in [0,1]#?

By signing up, you agree to our Terms of Service and Privacy Policy

To find the arc length of the function ( f(x) = x^2e^{1/x} ) on the interval ( [0, 1] ), you would need to use the formula for arc length:

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

Where ( f'(x) ) is the derivative of ( f(x) ) with respect to ( x ).

First, find the derivative ( f'(x) ), then plug it into the formula along with the limits of integration ( a = 0 ) and ( b = 1 ), and integrate.

The derivative ( f'(x) ) can be found using the product rule and chain rule:

[ f'(x) = 2xe^{1/x} - \frac{1}{x^3} e^{1/x} ]

Now, plug ( f'(x) ) into the arc length formula:

[ L = \int_{0}^{1} \sqrt{1 + \left(2xe^{1/x} - \frac{1}{x^3} e^{1/x}\right)^2} , dx ]

Integrate this expression within the given limits to find the arc length of ( f(x) ) on the interval ( [0, 1] ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- How do slope fields work?
- How do you find the volume of the region enclosed by the curves #y=2/x#, #y=0#, #x=1#, #x=3# rotated about #y=-1#?
- How do you find the average value of the function for #f(x)=sqrtx+1/sqrtx, 1<=x<=9#?
- How do you graph exponential decay?
- How do you sketch a slope field for #dy/dx = (x + 1)^2/y#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7