Trigonometric Substitutions: Example 1

Find

displaymath34

Solution. It is easy to see that sine-substitution is the one to use. Set tex2html_wrap_inline36 or equivalently tex2html_wrap_inline38 . Then tex2html_wrap_inline40 which gives us

displaymath42

Easy calculations give

displaymath44

Technique of integration of powers of trigonometric functions give

displaymath46

which suggests the substitution tex2html_wrap_inline48 . Hence tex2html_wrap_inline50 which implies

displaymath52

Therefore, we have

displaymath54

This will not answer fully the problem because the answer should be given as a function of x. Since tex2html_wrap_inline58 , we get after easy simplifications

displaymath60

[Calculus] [Next Example]
[Geometry] [Algebra] [Trigonometry ]
[Differential Equations] [Complex Variables] [Matrix Algebra]

S.O.S MATHematics home page

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Author: Mohamed Amine Khamsi

Copyright 1999-2017 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour