JSFiddle - React, Tailwind, and code Playground

HTML

<script src="//maxcdn.bootstrapcdn.com/bootstrap/3.3.6/js/bootstrap.min.js"></script>
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap.min.css">
<div id="carousel-example-generic" class="carousel slide" data-ride="carousel">
  <!-- Indicators -->
  <ol class="carousel-indicators">
    <li data-target="#carousel-example-generic" data-slide-to="0" class="active"></li>
    <li data-target="#carousel-example-generic" data-slide-to="1"></li>
    <li data-target="#carousel-example-generic" data-slide-to="2"></li>
  </ol>

  <!-- Wrapper for slides -->
  <div class="carousel-inner" role="listbox">
    <div class="item active">
        <div class="middle">
          <img src="http://placehold.it/1920x500">
        </div>
    </div>
    <div class="item">
        <div class="middle">
          <img src="http://placehold.it/1920x300">
        </div>
    </div>
    <div class="item">
        <div class="middle">
          <img src="http://placehold.it/600x900">
        </div>
    </div>
  </div>

  <!-- Controls -->
  <a class="left carousel-control" href="#carousel-example-generic" role="button" data-slide="prev">
    <span class="glyphicon glyphicon-chevron-left" aria-hidden="true"></span>
    <span class="sr-only">Previous</span>
  </a>
  <a class="right carousel-control" href="#carousel-example-generic" role="button" data-slide="next">
    <span class="glyphicon glyphicon-chevron-right" aria-hidden="true"></span>
    <span class="sr-only">Next</span>
  </a>
</div>

CSS

.carousel {
  width: 500px;
  height: 300px;
}

.middle {
  position: relative;
  height:300px;
}

.middle img {
  max-width: 100%;
  max-height:100%;
  margin: auto;
  position: absolute;
  left: 0;
  right: 0;
  top: 0;
  bottom: 0;
}