Thursday, January 19, 2017

integral of sqrt{[1-sqrt(x)] / [1+sqrt(x)]}

integral of sqrt{[1-sqrt(x)] / [1+sqrt(x)]}

use the substitution sqrt(x) = cost

use trigonometric formulae to simplify [1-cos t]  and [ 1+ cos t], sint using the half angle formulae

cancel off the common factors

simplify then again use trigonometric formulae to change the square terms to first degree expressions before integrating.

again use trigonometric formulae to change the variable back to x



trigonometric identities 

formulae on integration
 
PAGE 1 BASIC INTEGRATION

PAGE 2 INTEGRATION BY SUBSTITUTION

 PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR


PAGE 6 INTEGRATION USING PARTIAL FRACTIONS

disclaimer:
There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work

No comments:

Post a Comment

please leave your comments