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anonymous
 one year ago
Integration help
anonymous
 one year ago
Integration help

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1442609775803:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i have the answer as 9.747 rounded to 3 decimal places but i dont understand how to get

Zarkon
 one year ago
Best ResponseYou've already chosen the best response.2\[x=\frac{\tan(\theta)}{2}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i need explanation please

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2It's hard to take the root of a sum... that addition sign is causing a problem. We would like to apply some type of trigonometric substitution because our trig identities allow us to get rid of addition/subtraction. \(\rm 1\sin^2x=\cos^2x\) \(\rm 1+\tan^2x=\sec^2x\) And the others..

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Our problem involves something of the form: \(\rm 1+stuff^2\) Which is telling us that we want to use the tangent identity, ya?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2\[\large\rm \int\limits\sqrt{1+4x^2}~dx=\int\limits\sqrt{1+(2x)^2}~dx\]We would like to turn the 2x into tangent, then we would have 1+tangent^2 under the root, and would be able to apply our identity!

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2So, as Zarkon indicated, make the substitution, \(\large\rm 2x=\tan\theta\)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2So we're making the substitution: \(\large\rm \color{orangered}{2x=\tan\theta}\) Then our integral becomes:\[\large\rm \int\limits\limits\sqrt{1+(\color{orangered}{2x})^2}~dx=\int\limits\limits\sqrt{1+(\color{orangered}{\tan\theta})^2}~dx\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2We need to also replace the dx with something involving d(theta) though.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Whatchu think mage? :O Too confusing?
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