stuck in arc length problem

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stuck in arc length problem

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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1 Attachment
how does it get the 2650/4 + 441x/4?

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im getting 1325/2 on my calculator
|dw:1434600730609:dw|
2650/4=1325/2
but then why didnt the person put 1325/2 in the problem?
it looks like they wanted to pull the 1/4 out from under the radical.
oh i see
one more thing
what did he do here?
1 Attachment
like how did he get the 3+y=(1/8)tangent(theta)?
that's a trig substitution from right angle trig. basically if you have an integral of the form \[\sqrt{b^2+a^2x^2}\]you can make the substitution x = (a/b) tan Θ
I reversed that. x = (b/a) tan Θ
so the x is (3+y), the b is 1 and a is 8? right?
yes
okay thanks
you're welcome

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