Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2013 / Paper 2 / 20 / a / Solution

Under the regularity and integrability conditions for the Leibniz integral rule,

\frac{d}{d θ} \int_{a (θ)}^{b (θ)} f (x, θ) d x = f (b (θ), θ) b^{'} (θ) - f (a (θ), θ) a^{'} (θ) + \int_{a (θ)}^{b (θ)} \frac{\partial f}{\partial θ} (x, θ) d x .

The first two terms account for the moving endpoints; the last accounts for the integrand's own parameter dependence.

 Ancestors (13)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version