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Homework Help Overview

The discussion revolves around evaluating an integral and ensuring proper notation and limits during the integration process. The subject area includes calculus, specifically focusing on antiderivatives and integration techniques.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are examining the correct evaluation of an antiderivative and the proper use of differentials in integration. There are questions about specific lines in the evaluation process and whether the limits of integration are correctly noted.

Discussion Status

The discussion includes clarifications on the evaluation order of the antiderivative and the necessity of including differentials. Some participants are seeking confirmation on the final answer, while others are providing feedback on previous posts. There is no explicit consensus on the final answer yet, but guidance has been offered regarding the evaluation process.

Contextual Notes

Participants are working within the constraints of homework rules, which may limit the extent of guidance provided. There is an ongoing discussion about the accuracy of specific lines in the calculations and the implications of using differentials.

manal950
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You have a mistake on the next-to-last line. You have evaluated your antiderivative in the wrong order. Inside the parentheses you should have ln(sin(##\pi/2##)) - ln(sin(##\pi/6##)).

Also, the differential -- dx or du -- should appear in every step until you actually get the antiderivative.

When you make your substitution, that's when you should either change your limits of integration or at least make a note that the limits are values of x, not u. Here's what I mean:

$$ \pi \int_{x = \pi/6}^{\pi/2} \frac{du}{u}$$

By including "x = ..." in one of the limits of integration, that reminds you not to use them directly in the antiderivative that you get.
 
which line I got mistake is last line or what ?
 
manal950 said:
which line I got mistake is last line or what ?

I said which line in my last post.
Mark44 said:
You have a mistake on the next-to-last line. You have evaluated your antiderivative in the wrong order. Inside the parentheses you should have ln(sin(##\pi/2##)) - ln(sin(##\pi/6##)).
 
Mark44 said:
...

Also, the differential -- dx or du -- should appear in every step until you actually get the antiderivative.

...
I pointed out this same omission in your previous thread.
 
Is the final answer is = 2.17 ?
 
Is the final answer will be = 2.17 ?

anyone help ?
 
If you round to 2 decimal places, the answer is 2.18.
 

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