As described in the previous example, when the integrand includes certain radical expressions, a set of trigonmetric substitutions can be used. We follow the 'recipe' of the substitution rule. This 'recipe' helps us to convert the function from one expressed in terms of 'x' to a function of angle Θ. Once the conversion has been made, basic trigonometric identities are used to solve for the variable values. We then, solve the integration for the function expressed in terms of Θ, and finally replace the original variables into the result. For example, here we evaluate:
d x 36 + x 2
Radicals and Trigonmetric Substitutions (#2)
Show sender reference
Log in to my Electric Book site.
X Y a o h Θ 36+x 2 x 6

Electric Book-Link (e-Blink) URL:

The URL listed above can be inserted into your postings or e-mails; it will point to the text or area of the graph that you have selected.
To insert the link:

  • Drag your mouse across any text in the green problem area, or
  • Drag your mouse to form a selection box on the green graph area
  • Open the e-Blink tab to display this tab.
  • Copy the text above to your clipboard
  • When editing a note to your community or editing your e-mail, select some text and press the link button.
  • Paste your link into the text box for the URL.