How do you find the arc length of the curve #y=sqrt(x-3)# over the interval [3,10]?
Arc length will be approximately
Recall that arc length of a curve is given by
This is a pretty complex integral, so I would solve using a graphing calculator.
Hopefully this helps!
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To find the arc length of the curve ( y = \sqrt{x - 3} ) over the interval ([3, 10]), follow these steps:
- Compute the derivative of the function to find the differential element.
- Integrate the square root of (1 + (f'(x))^2) over the given interval.
Starting with the given function ( y = \sqrt{x - 3} ):
- Compute the derivative, ( y' ):
[ y' = \frac{1}{2\sqrt{x - 3}} ]
- Square the derivative:
[ (y')^2 = \frac{1}{4(x - 3)} ]
- Integrate ( \sqrt{1 + (y')^2} ) over the interval ([3, 10]):
[ \text{Arc Length} = \int_{3}^{10} \sqrt{1 + \frac{1}{4(x - 3)}} , dx ]
- Evaluate the integral.
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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.
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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- Find the volume of the solid via cross-sections?

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