From the image, it appears you are working on a calculus problem involving the length of a curve, and the given function is:

$L = \int_{0}^{\frac{\pi}{2}} \sqrt{1 + \left( \frac{dy}{dx} \right)^2} \, dx$

To clarify and solve this, let's first break down the process of finding the arc length of a curve.

Arc Length Formula:

For a curve described by $y = f(x)$, the arc length $L$ between two points $x = a$ and $x = b$ is given by the formula:

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

From the image, it seems the problem is asking you to find the length of the curve from $x = 0$ to $x = \frac{\pi}{2}$, where a function is provided (not fully visible).

Solution Outline:

1. Differentiate the function $y = f(x)$ with respect to $x$ to find $\frac{dy}{dx}$.
2. Substitute $\frac{dy}{dx}$ into the arc length formula.
3. Simplify the expression inside the square root.
4. Integrate the simplified expression from $x = 0$ to $x = \frac{\pi}{2}$.

If you provide the specific function $f(x)$, I can proceed with the exact differentiation and calculation of the arc length.

Would you like me to help further with this process or clarify any steps? Feel free to upload additional details.

Related Questions:

1. What is the given function $y = f(x)$ in your problem?
2. Have you learned about the arc length formula before, or is this a new concept for you?
3. Are there any specific steps in differentiation you need help with?
4. Would you like to see an example of an arc length calculation with a different function?
5. Do you know how to integrate functions that involve square roots, or would you like an explanation?

Tip:

For complex integrals involving square roots, it is helpful to check if trigonometric substitution or another simplification technique can be applied!