Find the arc length of the graph of the function over the interval [1,2].
Without telling us what the function is, how do you expect us to come up with an answer?
To find the arc length of the graph of a function over an interval, you can use the formula:
\[L = \int_a^b \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx\]
where \(L\) is the arc length, \(a\) and \(b\) are the endpoints of the interval, and \(\frac{dy}{dx}\) is the derivative of the function.
In this case, we need to find the arc length of the graph of a function over the interval [1,2]. Let's call the function \(f(x)\).
1. Start by finding the derivative of the function \(f(x)\). Let's call this derivative \(f'(x)\).
2. Then, calculate \(\left(\frac{dy}{dx}\right)^2\) as \(\left(f'(x)\right)^2\).
3. Now, substitute the values \(a = 1\) and \(b = 2\) into the formula:
\[L = \int_1^2 \sqrt{1 + \left(\left(f'(x)\right)^2\right)} \, dx\]
4. Evaluate the integral to find the arc length \(L\).