Register to reply

Integration of irrational function

by KLscilevothma
Tags: function, integration, irrational
Share this thread:
KLscilevothma
#1
Jun7-03, 11:39 PM
P: 321
Here's the question that I got stuck:

[inte]sqrt[x/(a-x)] dx ......................................(*)

I tried to use the following substitution
u=sqrt[x/(a-x)] and .........................................(1)
dx = 2u(1-a)/(1+u2)2 du................(2)

sub (1) and (2) into (*), after a few steps, I got

(2-2a)[inte]du/(1+u2) - 2(1-a)[inte]du/(u2+1)2

The answer derived from the first part, (2-2a)[inte]du/(1+u2), contains tan -1 but the model answer of this question is
-[squ](ax-x2) + a/2sin-1[(2x+a)/a] + C
For the second part, I let u = tan θ and got a strange expression.

Is my approach correct and is the final answer obtained from the above method differs the model answer only by the constant of integration ? Or am I using a wrong substitution?
Phys.Org News Partner Mathematics news on Phys.org
Heat distributions help researchers to understand curved space
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture
Hurkyl
#2
Jun8-03, 09:17 AM
Emeritus
Sci Advisor
PF Gold
Hurkyl's Avatar
P: 16,091
Check your work on your substitution.
KLscilevothma
#3
Jun9-03, 07:00 AM
P: 321
u=sqrt[x/(a-x)]

dx = 2au/(1+u2)2 du

thanks


Register to reply

Related Discussions
Proof: x is irrational => sqrt(x) is irrational Introductory Physics Homework 3
Proving Integral of an Irrational Function Calculus & Beyond Homework 5
Integration of the function exp(cos(x)) Differential Equations 7
Integration with a step function? Calculus & Beyond Homework 19
Differentiate an integration of a function with respect to that function itself Calculus 1