Trouble seeing the difference between autograder answer and my own

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Summary, The conversation is about a practice quiz question involving a trigonometric substitution to solve an integral. The person is confused about why the autograder marked their answer as incorrect, when it appears to be the same as the correct answer. However, they acknowledge that they may be forgetting a property of logarithms.
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Homework Statement
Integrate ##\frac{1}{\sqrt{x^2-49}}dx##
Relevant Equations
Trig sub, secant.
I was doing a practice quiz and got the following integral:

##\int \frac{1}{\sqrt{x^2-49}}dx##

Following normal trig sub. Using ##b^2 = c^2 - a^2## we find ##\sec{\theta} = \frac{x}{5}## and so ##x = 5\sec{\theta}## and ##dx = 5\sec{\theta}\tan{\theta}d\theta##

Then

## \int \frac{1}{\sqrt{x^2-49}}dx = 5 \int \frac{\sec{\theta}\tan{\theta}d\theta}{\tan{\theta}}##

Then after simplification:

##\int \sec{\theta}d\theta = ln|\sec{\theta} + \tan{\theta}| + C##

and solving for theta using the triangle:

## ln|\frac{x}{7} + \frac{\sqrt{x^2-49}}{7}| + C ##

The autograder marked me wrong. The correct answer was:

##ln|\frac{1}{7}(\sqrt{x^2-49} + x)| + C##

Which looks to be the same to me. I cannot see the difference. Even the plots look the same. I must be forgetting a property of logs that makes these distinct. Can you help me?
 
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  • #2
I'm assuming an autograder is some software? If so, its answer looks neater to me, but the answers are clearly equivalent.
 
  • #3
Some autograders are just ... sub-par ...
 

FAQ: Trouble seeing the difference between autograder answer and my own

What could be causing me to have trouble seeing the difference between the autograder answer and my own?

There could be several reasons for this. It is possible that there is a mistake in your code that is causing it to produce incorrect results. It is also possible that the autograder is using different test cases or a different method of evaluation than what you are using. Additionally, it could be an issue with your understanding of the problem or the language itself.

How can I improve my ability to spot the differences between my answer and the autograder's?

One way to improve is to carefully review your code and make sure you understand each line and its purpose. You can also try debugging your code and comparing it to the expected output. Another helpful technique is to practice with similar problems and compare your solutions to those of others.

Is it common to have trouble differentiating between my answer and the autograder's?

Yes, it is common for students to struggle with this. Programming can be complex and there are often multiple ways to solve a problem. It is important to carefully read and understand the instructions and compare your code to the expected output to identify any discrepancies.

How can I avoid confusion between my answer and the autograder's in the future?

One way to avoid confusion is to double check your code before submitting it. Make sure you understand the problem and have thoroughly tested your code. It can also be helpful to seek feedback from a peer or instructor to catch any mistakes you may have missed.

What should I do if I still can't see the difference between my answer and the autograder's?

If you are still having trouble, it may be beneficial to reach out to your instructor or a tutor for assistance. They can provide additional guidance and help you identify any mistakes in your code. It is also important to not get discouraged and continue practicing and learning from your mistakes.

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