Dumb integral question, can be answered (or hinted) in 2 seconds no doubt.

Click For Summary

Homework Help Overview

The discussion revolves around finding the anti-derivative of the function y=50/(25+x^2) in the context of calculating areas between curves. Participants express uncertainty about the integration techniques applicable to this function.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the challenges of rewriting the function for integration, questioning the applicability of u-substitution and the natural logarithm. There is mention of the need for a trigonometric substitution and uncertainty about the anti-derivative form.

Discussion Status

Some participants have suggested that a trigonometric substitution may be necessary, while others express confusion about this approach, indicating a lack of familiarity with it. The discussion is ongoing, with various interpretations of the integration process being explored.

Contextual Notes

There is a mention of the original poster's concern about division by zero and the implications of constants in logarithmic integration. Additionally, a question regarding the real values of the expression (25+x^2) is raised, hinting at underlying assumptions about the function's behavior.

Vagabond7
Messages
50
Reaction score
11

Homework Statement



Ok, so I am doing areas between curves, but one of the functions is y=50/(25+x^2)

This is stupid, but I THINK I am having trouble finding the anti-derivative (I just know my final answer is wrong, but I'm pretty sure it is related to this.)



The Attempt at a Solution



Ok, so obvious I can't rewrite as a negative power, leads to division by 0. I don't think u substitution works here because the derivative of u is not there (or there but off by a constant factor). Integrating as a natural log seems fine, but does that make the anti-derivative 50 ln (25+x^2)? That doesn't seem right.

In all the problems I did for log anti-derivatives I don't remember what to do if the 1/x is multiplied by a constant. Suggestions?
 
Physics news on Phys.org
Vagabond7 said:

Homework Statement



Ok, so I am doing areas between curves, but one of the functions is y=50/(25+x^2)

This is stupid, but I THINK I am having trouble finding the anti-derivative (I just know my final answer is wrong, but I'm pretty sure it is related to this.)



The Attempt at a Solution



Ok, so obvious I can't rewrite as a negative power, leads to division by 0. I don't think u substitution works here because the derivative of u is not there (or there but off by a constant factor). Integrating as a natural log seems fine, but does that make the anti-derivative 50 ln (25+x^2)? That doesn't seem right.

In all the problems I did for log anti-derivatives I don't remember what to do if the 1/x is multiplied by a constant. Suggestions?

If you want to integrate y you need a trig substitution. Like x=5*tan(t).
 
So you're saying that I can't find the antiderivative of 50/(25+x^2) without using some kind of trig substitution? I don't think I've ever even encountered that in my classes yet.
 
Vagabond7 said:
So you're saying that I can't find the antiderivative of 50/(25+x^2) without using some kind of trig substitution? I don't think I've ever even encountered that in my classes yet.

I'm afraid not. The antiderivative is an arctangent.
 
For what values of x does the expression (25+x^2) = 0?

Hint: They're not real.
 

Similar threads

Volume of solid region double integral
  • · Replies 27 ·
Replies
27
Views
3K
A doubt in Partial fraction decomposition
  • · Replies 8 ·
Replies
8
Views
2K
Please evaluate this double integral over rectangular bounds
  • · Replies 10 ·
Replies
10
Views
2K
Wolfram gave me one answer, examiners gave me another
  • · Replies 4 ·
Replies
4
Views
1K
U-Substitution in trig integral
  • · Replies 3 ·
Replies
3
Views
3K
Solve the homogeneous ODE: dy/dx = (x^2 + y^2)/xy
  • · Replies 3 ·
Replies
3
Views
2K
How To Integrate 1/[sqrt (x^2 + 3x + 2)] dx?
  • · Replies 44 ·
2
Replies
44
Views
6K
Finding the Wrong Answer with Stokes' Theorem
  • · Replies 4 ·
Replies
4
Views
2K
Solving the Integral ∫dx/(1-x)
  • · Replies 3 ·
Replies
3
Views
2K
Integrals that keep me up at night
  • · Replies 22 ·
Replies
22
Views
3K