Integration question (1 Viewer)

[dulip]

just a textbook question


http://latex.codecogs.com/gif.latex...n\:for\:I_{n}\:in\:terms\:of\:n\:for\:n\geq 0

You don't have to write out a full solution unless you really want to, just try point me in the right direction if you can

 

[Carrotsticks]

Then let u = tan theta

Then continue from there.

Alternatively for that same integral, you could use Integration by Parts, making the choices:

 

[juantheron]

 

[dulip]

thanks, i'm finding it hard to know when/what to substitute
any tips?
also anyone able to help on the 2nd question (i linked it because it didn't post properly when i copied it)

 

[jet]

Well in this case, it's priority to remove the annoying square root, so carrotsticks got smart and let u² = stuff inside the square root. There's a good chance this will get rid of it.

I honestly have no idea how junatheron chose his substitution because I've never seen it done that way before.

I'll do the next question later if nobody else has done it by then.

 

[Drongoski]

Just saw this question


By inspection:







Did I make a mistake somewhere?

 

[Nooblet94]

Just saw this question


By inspection:







Did I make a mistake somewhere?

Yep, that derivative is equal to

 

[bleakarcher]

just one question. say you used the substitution x=sec^2(theta) would you end up in the denominator with abs[tan(theta)] or just tan(theta)?

I stumbled across this thought the other day. 4U Cambridge just tells me tan(theta).

 

[bleakarcher]

Anyone care to explain?

 

[Drongoski]

Yep, that derivative is equal to

Oh yeah - thanks. I thought I knew how to differentiate! I already had the feeling I made a mistake somewhere.

 

[jet]

Square root means positive square root, hence you don't need the absolute value.

 

[seanieg89]

Square root means positive square root, hence you don't need the absolute value.

I would think thats WHY abs value signs would be necessary. Say you were integrating over an interval where tan is negative...I remember Cambridge not doing this though so I don't know what the BOS expect.