Integration Q (1 Viewer)

[shaon0]

Re: 回复: Re: 回复: Re: 回复: Re: Integration Q

sorry but i need some help;
Integrate: xsqrt(4-x) dx

 

[lolokay]

Re: 回复: Re: 回复: Re: 回复: Re: Integration Q

just do i.b.p

 

[shaon0]

Re: 回复: Re: 回复: Re: 回复: Re: Integration Q

just do i.b.p

yeah i did
but i got some weird answer

 

[lolokay]

Re: 回复: Re: 回复: Re: 回复: Re: Integration Q

yeah i did
but i got some weird answer

let x=u, (4-x)^1/2 = dv
du = dx
v = -2/3(4-x)^3/2

so I x(4-x)^1/2.dx
= -2/3 x(4-x)^3/2 + I 2/3(4-x)^3/2
= -2/3 x(4-x)^3/2 - 4/15(4-x)^5/2
= (4-x)^3/2(-10/15 x - 16/15 + 4x/15)
= -2/15 (4-x)^3/2(3x + 8) [+C]

 

[shaon0]

Re: 回复: Re: 回复: Re: 回复: Re: Integration Q

let x=u, (4-x)^1/2 = dv
du = dx
v = -2/3(4-x)^3/2

so I x(4-x)^1/2.dx
= -2/3 x(4-x)^3/2 + I 2/3(4-x)^3/2
= -2/3 x(4-x)^3/2 - 4/15(4-x)^5/2
= (4-x)^3/2(-10/15 x - 16/15 + 4x/15)
= -2/15 (4-x)^3/2(3x + 8) [+C]

oh, i got what you got but i didn't simpligfy it any further from:
= -2/3 x(4-x)3/2 - 4/15(4-x)5/2
would i still get full marks for my answer?

 

[lolokay]

Re: 回复: Re: 回复: Re: 回复: Re: Integration Q

I assume you would, unless it said "in its simplest form" or something

 

[shaon0]

Re: 回复: Re: 回复: Re: 回复: Re: Integration Q

I assume you would, unless it said "in its simplest form" or something

Yes! thanks for your help

 

[Trebla]

sorry but i need some help;
Integrate: xsqrt(4-x) dx

You can avoid integration by parts using the following:
∫ x√(4 - x) dx = - ∫ ([4 - x] - 4)√(4 - x) dx
= - ∫ [4 - x]√(4 - x) dx + ∫ 4√(4 - x) dx
= - ∫ (4 - x)^3/2 dx + 4 ∫ (4 - x)^1/2 dx
= 2(4 - x)^5/2/5 - 8(4 - x)^3/2/3 + c

That should be the same answer if you factorise (4 - x)^3/2 and put over a common denominator.

 

[shaon0]

You can avoid integration by parts using the following:
∫ x√(4 - x) dx = - ∫ ([4 - x] - 4)√(4 - x) dx
= - ∫ [4 - x]√(4 - x) dx + ∫ 4√(4 - x) dx
= - ∫ (4 - x)^3/2 dx + 4 ∫ (4 - x)^1/2 dx
= 2(4 - x)^5/2/5 - 8(4 - x)^3/2/3 + c

That should be the same answer if you factorise (4 - x)^3/2 and put over a common denominator.

sorry, thats too pro for me

 

[tacogym27101990]

yeah i wouldn't use i.b.p for a question like this as its not two different functions really
u use ibp for things like e^x.sinx and stuff
you can just use a suitable substitution such as u=4-x
its alot quicker and easier

 

[lolokay]

well I wouldn't say it takes all that long to do it by parts.
I definitely prefer the u=4-x way though

 

[shaon0]

yeah i wouldn't use i.b.p for a question like this as its not two different functions really
u use ibp for things like e^x.sinx and stuff
you can just use a suitable substitution such as u=4-x
its alot quicker and easier

alrite, i'll take that on board. I wasn't thinking of substitution because it was in the i.b.p section of fitzpatrick.
anyways, Thanks for the advice