Integral Exercises

<body> <div align=center><img src="/banner2.gif" width=500 height=100 alt="MiraCosta College"></div> <h2>Math 115 - Calculus with Applications</h2> <h3>Integrals - Exercises with Guided Solutions</h3> <div>Steve Schaefer, Instructor</div> <p>This page contains some exercises to help you be more automatic with integrals. I suggest that you shrink this window down to a horizontal strip, so that most of the screen is open. When you click on the links below, it will display the content in a different window. Make that window a convenient size and place it directly above or below this one.</p> <h3>Elementary Integrals and Integration by Substitution<font face="times"></font></h3> <table border=1 cellpadding=5 width="100%" style="font-family: times"> <tr><td width="0%"></td><th>Integral</th><th>Method</th><th>First Step</th><th>Answer</th><th>Solution</th></tr> <tr align=center><td width="0%">(1)</td> <td> ∫ <i>dx</i> </td> <td><a href="integ1m.html" target="guide">Method</a></td> <td><a href="integ1f.html" target="guide">First Step</a></td> <td><a href="integ1a.html" target="guide">Answer</a></td> <td><a href="integ1s.html" target="guide">Solution</a></td> </tr> <tr align=center><td width="0%">(2)</td> <td> ∫ <i>x dx</i> </td> <td><a href="integ2m.html" target="guide">Method</a></td> <td><a href="integ2f.html" target="guide">First Step</a></td> <td><a href="integ2a.html" target="guide">Answer</a></td> <td><a href="integ2s.html" target="guide">Solution</a></td> </tr> <tr align=center><td width="0%">(3)</td> <td> ∫ <i>x</i><sup>4</sup> <i>dx</i> </td> <td><a href="integ3m.html" target="guide">Method</a></td> <td><a href="integ3f.html" target="guide">First Step</a></td> <td><a href="integ3a.html" target="guide">Answer</a></td> <td><a href="integ3s.html" target="guide">Solution</a></td> </tr> <tr align=center><td width="0%">(4)</td> <td> ∫ 5 <i>dx</i> </td> <td><a href="integ4m.html" target="guide">Method</a></td> <td><a href="integ4f.html" target="guide">First Step</a></td> <td><a href="integ4a.html" target="guide">Answer</a></td> <td><a href="integ4s.html" target="guide">Solution</a></td> </tr> <tr align=center><td width="0%">(5)</td> <td> ∫ 7<i>x</i><sup>–2</sup> <i>dx</i> </td> <td><a href="integ5m.html" target="guide">Method</a></td> <td><a href="integ5f.html" target="guide">First Step</a></td> <td><a href="integ5a.html" target="guide">Answer</a></td> <td><a href="integ5s.html" target="guide">Solution</a></td> </tr> <tr align=center><td width="0%">(6)</td> <td><table border=0 cellspacing=0 cellpadding=0><tr> <td>∫ – </td> <td align=center>3<sup></sup><hr noshade size=1><i>x</i><sup>3</sup></td> <td>  <i>dx</i></td> </tr></table></td> <td><a href="integ6m.html" target="guide">Method</a></td> <td><a href="integ6f.html" target="guide">First Step</a></td> <td><a href="integ6a.html" target="guide">Answer</a></td> <td><a href="integ6s.html" target="guide">Solution</a></td> </tr> <tr align=center><td width="0%">(7)</td> <td><table border=0 cellspacing=0 cellpadding=0><tr> <td>∫ –4  </td> <td align=center><sup></sup>√<i>x</i><hr noshade size=1><i>x</i><sub></sub></td> <td>  <i>dx</i></td> </tr></table></td> <td><a href="integ7m.html" target="guide">Method</a></td> <td><a href="integ7f.html" target="guide">First Step</a></td> <td><a href="integ7a.html" target="guide">Answer</a></td> <td><a href="integ7s.html" target="guide">Solution</a></td> </tr> <tr align=center><td width="0%">(8)</td> <td><table border=0 cellspacing=0 cellpadding=0><tr> <td>∫  </td> <td align=center>(1 + √<i>x</i>)<sup>2</sup><hr noshade size=1><i>x</i><sup>3/2</sup></td> <td>  <i>dx</i></td> </tr></table></td> <td><a href="integ8m.html" target="guide">Method</a></td> <td><a href="integ8f.html" target="guide">First Step</a></td> <td><a href="integ8a.html" target="guide">Answer</a></td> <td><a href="integ8s.html" target="guide">Solution</a></td> </tr> <tr align=center><td width="0%">(9)</td> <td><table border=0 cellspacing=0 cellpadding=0><tr> <td>∫ <i>e<sup>x</sup> <i>dx</i></td> </tr></table></td> <td><a href="integ9m.html" target="guide">Method</a></td> <td><a href="integ9f.html" target="guide">First Step</a></td> <td><a href="integ9a.html" target="guide">Answer</a></td> <td><a href="integ9s.html" target="guide">Solution</a></td> </tr> <tr align=center><td width="0%">(10)</td> <td><table border=0 cellspacing=0 cellpadding=0><tr> <td>∫ 3<i>e<sup>2x</sup> <i>dx</i></td> </tr></table></td> <td><a href="integ10m.html" target="guide">Method</a></td> <td><a href="integ10f.html" target="guide">First Step</a></td> <td><a href="integ10a.html" target="guide">Answer</a></td> <td><a href="integ10s.html" target="guide">Solution</a></td> </tr> <tr align=center><td width="0%">(11)</td> <td><table border=0 cellspacing=0 cellpadding=0><tr> <td>∫  </td> <td align=center>6<i>x</i><sup>2</sup> <i>dx</i><hr noshade size=1>(2<i>x</i><sup>3</sup> + 7)<sup>3/2</sup></td> </tr></table></td> <td><a href="integ11m.html" target="guide">Method</a></td> <td><a href="integ11f.html" target="guide">First Step</a></td> <td><a href="integ11a.html" target="guide">Answer</a></td> <td><a href="integ11s.html" target="guide">Solution</a></td> </tr> </table> </body>