Ask your own question, for FREE!
Calculus1 12 Online
OpenStudy (anonymous):

Could someone please help me with the integration of this, please? int_{1}^{4}sqrt{1+(\frac{ 1 }{2sqrt{y} }-9)^2} (see the equation in the comments)

OpenStudy (anonymous):

\[\int\limits_{1}^{4}\sqrt{1+(\frac{ 1 }{2\sqrt{y} }-9)^2}\]

OpenStudy (anonymous):

I'm wondering if a trig sub might be useful here: \[\frac{1}{2\sqrt y}-9=\tan u~~~~\iff~~~~\frac{1}{y}=4(\tan u+9)^2\\ -\frac{1}{4y^{3/2}}dy=\sec u \tan u~du\\ -\frac{1}{2y}\left(\frac{1}{2\sqrt y}\right)dy=\sec u \tan u~du\\ -\frac{4(\tan u+9)^2}{2}\left(\tan u+9\right)~dy=\sec u \tan u~du\\ -2(\tan u+9)^3~dy=\sec u \tan u~du\\ dy=-\frac{\sec u \tan u}{2(\tan u+9)^3}~du\] So the integral would change from \[{\huge \int}_1^4\sqrt{1+\left(\frac{1}{2\sqrt y}-9\right)^2}~dy\] to \[{\huge \int}_?^?\sqrt{1+\tan^2u}~\left(-\frac{\sec u \tan u}{2(\tan u+9)^3}~du\right)\] Some simplifying: \[-\frac{1}{2}{\huge \int}_?^?\frac{\sec^2 u \tan u}{(\tan u+9)^3}~du\] Then another substitution: \[t=\tan u~~\Rightarrow~~dt=\sec^2 u~du\] \[-\frac{1}{2}{\huge \int}_?^?\frac{t}{(t+9)^3}~dt\] I'm not too sure about the limits just yet... and not entirely sure the trig sub is valid, but I'll look it over some.

OpenStudy (anonymous):

An integral from hell. Refer to the Mathematica 9 Home Edition attachment.

OpenStudy (anonymous):

thank you both!!

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
Countless7Echos: Ah trying out the whole T.V girl drawing :p (I love drawing eyes)
54 minutes ago 7 Replies 5 Medals
kaelynw: starting to draw a hand
1 day ago 16 Replies 2 Medals
Twaylor: Rate it :D (Took 2 days)
2 days ago 7 Replies 0 Medals
XShawtyX: Art, Short Writing Assignment: Imagining Landscapes
1 hour ago 7 Replies 1 Medal
XShawtyX: Chemistry, Help ud83dude4fud83cudffe
3 days ago 13 Replies 1 Medal
kaelynw: tried a lil smt, the arm is off but i like the other stuff
3 days ago 27 Replies 3 Medals
kaelynw: art igg
3 days ago 14 Replies 1 Medal
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!