Question

arc length

Answer 1

could someone clarify what my teacher did to get to the next BLUE box ?

Answer 2

added

Answer 3

how so? for some reason i don't see how she did it! did she integrate??

Answer 4

\[\sqrt{1+\frac{1}{36}}=\sqrt{\frac{37}{36}}=\frac{1}{6}\sqrt{37}\]

Answer 5

yes @satellite73 i understand that part but as far as how she integrated I'm a little confused?

Answer 6

for example, how did the 1/6 go away?

Answer 7

a mental u sub i think

Answer 8

ahhhhh i see it now. and the radical 37 was pulled out b/c it was a constant so thats why its still there

Answer 9

\(u=\frac{\theta}{6}\) so \(du=\frac{d\theta}{6}\) and \(6du=d\theta\)

Answer 10

6's go bye bye
the \(\sqrt{37}\) is a constant

Answer 11

@satellite73 got it :) thank you!

Answer 12

i wish all math was this easy!
arc length problems have to be cooked up completely to make the integration possible

Answer 13

yw