Stuck on integration problem Watch

bobbricks
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#1
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#1
Find the area of the region bounded by the curve with equation
25=ysqrt(25+x^2) and the lines x=+-5.

I used the substitution x=5tanu
si Integral= [25/sqrt(25+25tan2u)]sec2 u du
This simplifies down to Integral=5secu
so I integrated that to get ln[secu+tanu] with the limits from -pi/4 (bottom limit) to pi/4 (top limit).

But this does not give the right answer (44) ...?
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Notnek
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#2
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(Original post by bobbricks)
Find the area of the region bounded by the curve with equation
25=sqrt(25+x^2) and the lines x=+-5.

I used the substitution x=5tanu
si Integral= [25/sqrt(25+25tan2u)]sec2 u du
This simplifies down to Integral=5secu
so I integrated that to get ln[secu+tanu] with the limits from -pi/4 (bottom limit) to pi/4 (top limit).

But this does not give the right answer (44) ...?
Can you check you've posted the question correctly? There's no y in your curve equation. And is the region bounded by another line e.g. the x-axis?
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bobbricks
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(Original post by notnek)
Can you check you've posted the question correctly? There's no y in your curve equation. And is the region bounded by another line e.g. the x-axis?
Sorry, it should be:
25=ysqrt(25+x^2)
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the bear
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(Original post by bobbricks)
Sorry, it should be:
25=ysqrt(25+x^2)
it still does not look right... why is it not y = .... ?
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ghostwalker
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#5
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(Original post by bobbricks)

I used the substitution x=5tanu
si Integral= [25/sqrt(25+25tan2u)]5sec2 u du
You missed a factor of 5 - in red.
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bobbricks
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(Original post by the bear)
it still does not look right... why is it not y = .... ?
That's how the question was given:
you can rearrange it to y=25/sqrt(25+x^2)
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bobbricks
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#7
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(Original post by ghostwalker)
You missed a factor of 5 - in red.
Okay, so it should get to Integral of 25secu which becomes 25ln(secu+tanu) ...?

Are the limits still u=-pi/4 to u=pi/4 since that still doesn't give the correct answer?
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ghostwalker
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(Original post by bobbricks)
Okay, so it should get to Integral of 25secu which becomes 25ln(secu+tanu) ...?
Yep.

Are the limits still u=-pi/4 to u=pi/4 since that still doesn't give the correct answer?
Yes. Came to 44 (2 sig fig) when I did it. Calculator problem?
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Notnek
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(Original post by bobbricks)
Okay, so it should get to Integral of 25secu which becomes 25ln(secu+tanu) ...?

Are the limits still u=-pi/4 to u=pi/4 since that still doesn't give the correct answer?
That will lead to the correct answer now. Try working it out again.
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bobbricks
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#10
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Thanks guys it does work
However, why is it that you can't use the bottom limit as 3pi/4 instead of -pi/4 since that will not give the correct answer?
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