Derivatives and Integrals: An Annotated Discourse

<solution>
  <p>
    If your exercise feels like proving a theorem,
    then you might want to make some comments,
    but also clearly delineate which part of the solution is a the complete proof.
  </p>
  <proof>
    <p>
      Lorem ipsum dolor sit amet, consectetur adipiscing elit.
      Proin lorem diam, convallis in nulla sed, accumsan fermentum urna.
      Pellentesque aliquet leo elit,
      ut consequat nunc dapibus ac.
      Sed lobortis leo tincidunt, vulputate nunc at, ultricies leo.
      Vivamus purus diam,
      tristique laoreet purus eget, mollis gravida sapien.
      Nunc vulputate nisl ac mauris hendrerit cursus.
      Sed vel molestie velit.
      Suspendisse sem sem, elementum at vehicula id, volutpat ac mi.
      Nullam ullamcorper fringilla purus in accumsan.
      Mauris at nunc accumsan orci dictum vulputate id id augue.
      Suspendisse at dignissim elit, non euismod nunc.
      Aliquam faucibus magna ac molestie semper.
      Aliquam hendrerit sem sit amet metus congue tempor.
      Donec laoreet laoreet metus, id interdum purus mattis vulputate.
      Proin condimentum vitae erat varius mollis.
      Donec venenatis libero sed turpis pretium tempor.
    </p>
    <p>
      Praesent rutrum scelerisque felis sit amet adipiscing.
      Phasellus in mollis velit.
      Nunc malesuada felis sit amet massa cursus,
      eget elementum neque viverra.
      Integer sagittis dictum turpis vel aliquet.
      Fusce ut suscipit dolor, nec tristique nisl.
      Aenean luctus, leo et ornare fermentum,
      nibh dui vulputate leo, nec tincidunt augue ipsum sed odio.
      Nunc non erat sollicitudin, iaculis eros consequat, dapibus eros.
    </p>
  </proof>
</solution>

<solution>
  <p>
    This solution will migrate to a list of solutions in the backmatter.
    We include a <c>sidebyside</c> as a test.
  </p>
  <sidebyside width="30%">
    <p>
      This is a skinny paragraph which should be just 30% of the width.
    </p>
    <p>
      And another skinny paragraph which should also be just 30% of the width.
    </p>
  </sidebyside>
</solution>

<solution>
  <p>
    Maybe a global switch should be used to suppress solutions,
    while a separate processing regime could use them as part of a solutions manual.
  </p>
</solution>

<solution xml:id="solution-antiderivative">
  <p>
    An antiderivative of <m>x^2</m> is <m>F(x)=x^3/3</m>, so by the FTC,
    <me>
      \definiteintegral{2}{4}{x^2}{x}=F(4)-F(2)=\frac{1}{3}\left(4^3-2^3\right)=\frac{56}{3}
    </me>!?!
    This is indeed an exciting result,
    but we are mostly interested in seeing that the sentence-ending punctuation is absorbed properly into the displayed equation.
  </p>
</solution>

<solution>
  <p>
    We could prove either result first,
    then obtain the other as an easy consequence.
  </p>
</solution>