help: integrate x[(4-x)^0.5] (1 Viewer)

[wori]

I cannot get it right, so hand it over to you guys~

 

[who_loves_maths]

hi wori,

integrate x[Sqrt(4-x)]:

let (4-x) = u ---> du = -dx ---> x = (4-u)

so, Int[xSqrt(4-x)dx] = - Int[(4-u)Sqrt(u)du] = - Int[ 4u^(1/2) - u^(3/2)]

= -(8/3)(u^1.5) + (2/5)(u^2.5) + c = (2/5)[(4-x)^2][Sqrt(4-x)] -(8/3)[4-x][Sqrt(4-x)] + c

hope that helps

 

[turtle_2468]

Let u=4-x.

 

[~ ReNcH ~]

Or let x=4-u²

 

[haboozin]

this is a very common question that a lot of people get stuck in...

its bout the only one that u cant see instantly... just gotta memorize what to do i guess

 

[who_loves_maths]

Originally Posted by ~ Rench ~
Or let x=4-u^2

why would you do that? that the same as saying let u^2 = (4 -x)... but why do that when you can just let u = (4 -x)?

 

[turtle_2468]

I guess u=4-x is slightly more intuitive plus it saves ugliness in the substitution bit (only du=-dx). But slide rule does have a point, both work.. and in the 4U exam particularly, no matter how ugly the solution as long as it's right you'll get full marks for it.. (most maths exams in fact )

 

[velox]

u = 4-x is the only subsitution i thought of.

 

[who_loves_maths]

Originally Posted by Slide_Rule
Why not? Maths ain't black and white. Sort of.

yeah of course not. there are many elegant and differing methods of solving many maths problems. but for such an "easy" school-level problem, why strive to make life difficult for yourself? mathematics is best viewed in simplicity and elegance.

also, i was specifically refering to it in the context of 4u maths. in a test or exam, one would not gratuitously seek difficult ways of solving a problem when there exists a simpler method.

 

[FinalFantasy]

yeah of course not. there are many elegant and differing methods of solving many maths problems. but for such an "easy" school-level problem, why strive to make life difficult for yourself? mathematics is best viewed in simplicity and elegance.

also, i was specifically refering to it in the context of 4u maths. in a test or exam, one would not gratuitously seek difficult ways of solving a problem when there exists a simpler method.

man ur vocab is damn good lol
wat lvl english do u do

 

[Sphyx]

isnt this a standard 3u question? just integration by subst...

 

[who_loves_maths]

Originally Posted by FinalFantasy
man ur vocab is damn good lol
wat lvl english do u do?

lol? what vocab? every word in my last post are commonplace and ubiquitous.
you're just buttering me up cause i called you the integration-master aren't you?

i do simple english advanced at school; albeit not because i don't like english ext's, it's just that i like only doing 10 units more

 

[FinalFantasy]

lol? what vocab? every word in my last post are commonplace and ubiquitous.

LoL! just in this post.. the word "ubiquitous" is not "common.."... well not to me anyway! hahaha

 

[Antwan23q]

I = x[(4-x)^1/2]dx

Let u= 4-x
du= -dx

.: I = -(4-u)(u^1/2)du
= (u-4)(u^1/2)du
= [u^3/2 - 4u^1/2]du
= 2/5u^(5/2)-4(2/3)u^(3/2)+C
=2/5(4-x)^5/2 - 8/3(4-x)^3/2

ta da!

 

[~ ReNcH ~]

why would you do that? that the same as saying let u^2 = (4 -x)... but why do that when you can just let u = (4 -x)?

I just thought I would suggest it. When it comes to exam time, you're not always going to remember the appropriate substitution...or at least the one that is most efficient. And as others have said, why not? It doesn't make it any more difficult.

 

[rabdog]

the substitution is obvious here

 

[velox]

I guess u=4-x is slightly more intuitive plus it saves ugliness in the substitution bit (only du=-dx). But slide rule does have a point, both work.. and in the 4U exam particularly, no matter how ugly the solution as long as it's right you'll get full marks for it.. (most maths exams in fact )

Elegance is a skill in maths turtle. No harm in having an elegant solution.