Question

In Exercises \(1-20,\) find \(d y / d x\). $$y=\int_{3 \sqrt{2}}^{10} \ln \left(2+p^{2}\right) d p$$

Short answer

The derivative of the given integral with respect to x is 0.

Step-by-step solution

Identify variable of integration and limits of the integral

Here, the variable of integration is p and the limits of the integral are \(3\sqrt{2}\) and 10 which are constants.

Apply Leibniz Rule

According to Leibniz rule, the derivative of this integral with respect to any variable excluding the variable of integration (i.e. p) is 0 because the integral is a definite one and the upper and lower limits are constant.

Write the derivative

As we're required to find \(\frac{dy}{dx}\), the derivative of y with respect to x, and as inferred from Step 2, the derivative of this integral with respect to x will be 0.