Integrate (5x+2)dx/(x-2) from 0 to 1

  • Thread starter Thread starter erjkism
  • Start date Start date
  • Tags Tags
    Integrate
Click For Summary

Homework Help Overview

The problem involves integrating the function (5x+2)/(x-2) from 0 to 1. The discussion centers around techniques for simplifying the integrand to facilitate integration.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss various methods for simplifying the integrand, including splitting the fraction and using substitution. Some express uncertainty about the next steps after initial attempts.

Discussion Status

Several participants have offered different approaches to rewriting the integrand, suggesting that polynomial division and substitutions may be useful. There is an ongoing exploration of these ideas without a clear consensus on the best method.

Contextual Notes

Participants note the challenge of integrating over the specified limits and the potential need for substitutions or alternative algebraic manipulations. There is an acknowledgment of the complexity involved in the integration process.

erjkism
Messages
54
Reaction score
0

Homework Statement



\int\frac{(5x+2)dx}{x-2} from 0 to 1


Homework Equations



The Attempt at a Solution



I've tried splitting it up into (5x)/(x-2) + (2)/x-2), but i couldn't go any farter. Ived also tried using lots of U subsitutions, but i can't figure out what do next. Is there some trick that i am not seeing?
 
Physics news on Phys.org
Yep, the obvious one. u=x-2. dx=du. x=2+u.
 
Another way to split it up [without explicitly invoking a substitution]
is to write the numerator 5x+2 as 5(x-2)+12.
 
robphy said:
Another way to split it up [without explicitly invoking a substitution]
is to write the numerator 5x+2 as 5(x-2)+12.
Woah, woulda never thought of that. Nice, I want your vision :-]
 
robphy said:
Another way to split it up [without explicitly invoking a substitution]
is to write the numerator 5x+2 as 5(x-2)+12.

You'll still want u=x-2 to do the 12/(x-2) part.
 
Just do polynomial division. It becomes 5 + 12/(x - 2).

Oops.
 
Dick said:
You'll still want u=x-2 to do the 12/(x-2) part.

True... and now the substitution is really obvious.
 

Similar threads

Verify Green's Theorem in the given problem
  • · Replies 10 ·
Replies
10
Views
2K
Find the result of definite integration
  • · Replies 6 ·
Replies
6
Views
2K
Prove that the integral is equal to ##\pi^2/8##
  • · Replies 105 ·
4
Replies
105
Views
11K
Integral of 1 / (x^2 + 2) dx ?
  • · Replies 54 ·
2
Replies
54
Views
16K
Two Solutions for y' = 5x^3(y-1)^1/5 with Initial Condition y(0)=1
  • · Replies 11 ·
Replies
11
Views
2K
Series Convergence: What Can the Nth Term Test Tell Us?
  • · Replies 6 ·
Replies
6
Views
2K
Integrate [cosec(30°+x)-cosec(60°+x)] dx in terms of tan x
  • · Replies 3 ·
Replies
3
Views
2K
How to Integrate [1/(x^2 + 3)] dx?
  • · Replies 5 ·
Replies
5
Views
3K
Evaluate the given integrals - line integrals
  • · Replies 2 ·
Replies
2
Views
1K
Volume between a region (above x-axis and below parabola) and a surface
  • · Replies 4 ·
Replies
4
Views
3K