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The discussion focuses on correcting a mathematical error in evaluating an antiderivative involving limits of integration. The correct evaluation requires using ln(sin(π/2)) - ln(sin(π/6)) in the parentheses. Additionally, it emphasizes the necessity of including the differential (dx or du) at every step until the antiderivative is obtained. The final answer, when rounded to two decimal places, is confirmed to be 2.18.

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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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