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

In summary, the conversation discusses the difficulty of finding the anti-derivative of the function y=50/(25+x^2) and the possibility of using a trig substitution to solve it. The person suggests using a trig substitution and mentions that the antiderivative is an arctangent. The conversation ends with a hint about the values of x for which the expression (25+x^2) equals 0.
  • #1
Vagabond7
50
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?
 
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  • #2
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).
 
  • #3
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.
 
  • #4
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.
 
  • #5
For what values of x does the expression (25+x^2) = 0?

Hint: They're not real.
 

1. What is a dumb integral question?

A dumb integral question is a type of mathematical problem that can be easily answered or hinted at in a matter of seconds. It typically involves basic integration techniques and does not require complex problem-solving skills.

2. Can you give an example of a dumb integral question?

One example of a dumb integral question is: "What is the integral of x^2?" This can be easily answered by using the power rule of integration, which states that the integral of x^n is (x^(n+1))/(n+1).

3. How can I quickly solve a dumb integral question?

The key to quickly solving a dumb integral question is to have a good understanding of basic integration techniques, such as the power rule, substitution, and integration by parts. Practice and familiarity with these techniques will help you solve these types of questions in just a few seconds.

4. Can a dumb integral question be solved without using a calculator?

Yes, most dumb integral questions can be solved without using a calculator. These questions typically involve simple functions and can be solved by hand using basic integration techniques.

5. Are dumb integral questions useful in real-world applications?

While dumb integral questions may not have direct applications in real-world scenarios, they are important for building a strong foundation in calculus and understanding more complex integration problems. They also help develop critical thinking and problem-solving skills, which are useful in all areas of science and mathematics.

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