YAMT: If anyone wants do to integrals at night

[Ricemarine]

I am at a loss as to how to go about this equation

e^t * sqrt[25 - e^(2t)] dt

if u = e^t
du = e^t dt
dv = sqrt[25 - e^(2t)dt
v = 25/2 sin^-1 (e^x/5)

but if I plug v into the equation uv = int[v du], it's really messed up...
Wanna give a hand night shift?

 

[KLin]

Thanks, now my head hurts. :|

 

[LongCoolMother]

Are you sure you need to do integration by parts?

How about u=e^t
du = e^t dt

so it becomes

sqrt(25-u^2) du

and then trig substitution?

I could be wrong, im like half asleep and I didnt write it on paper or anything. just going off the top of my head.

 

[Ricemarine]

Originally posted by: KLin
Thanks, now my head hurts. :|

Gotta love calculus huh ...
or Calculus, B.C., whichever seems nicer at the moment.

 

[MmmSkyscraper]

I'd eat some cake.

 

[chuckywang]

First of all, the derivative of Arcsin(x) is 1/sqrt(1-x^2), not sqrt(1-x^2).

 

[chuckywang]

Second of all, you're on the wrong track to begin with. This problem requires a bunch of steps.

1) First let u = e^t, so du=e^t dt. Substituting, your integral now becomes sqrt(25-u^2) du.

2) Rewrite this integral as (25-u^2)/(sqrt(25-u^2)) du = 25/sqrt(25-u^2) du - u^2/(sqrt(25-u^2)) du

The integral of the first term is an Arcsin. The integral of the second term can be found either by integration by parts or trig substitution (let u = 5sin(theta)).

 

[Ricemarine]

Originally posted by: chuckywang
Second of all, you're on the wrong track to begin with. This problem requires a bunch of steps.

1) First let u = e^t, so du=e^t dt. Substituting, your integral now becomes sqrt(25-u^2) du.

2) Rewrite this integral as (25-u^2)/(sqrt(25-u^2)) du = 25/sqrt(25-u^2) du - u^2/(sqrt(25-u^2)) du

The integral of the first term is an Arcsin. The integral of the second term can be found either by integration by parts or trig substitution (let u = 5sin(theta)).

Ohhhhhhhhhhhhhh.................
Hum... I knew I went about it the wrong way...

Thanks chuckywang

 

[compuwiz1]

Nice read! This is the geeky stuff AT was born from.

 

[Dangerer]

Originally posted by: compuwiz1
Nice read! This is the geeky stuff AT was born from.

what? this is just basic calculus that most students learn in high school