Past exam of the mathematical methods II course of the University of Oxford / 2014 / 6

Table of contents
- Solution 6

Solution

The integration region is the triangle

0 \leq y \leq x \leq π

. Reversing its order gives

I = \int_{0}^{π} \int_{0}^{x} \frac{s i n x}{x} d y d x = \int_{0}^{π} sin x d x = 2.

The factor of

x

from the inner interval cancels the denominator. At

x = 0

,

sin x / x

has a removable singularity, so no divergent integral is being hidden by this change of order. Fubini's theorem applies to its continuous extension on the bounded triangle.

 Ancestors (10)

 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