I'm retarded, math people help

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I decided to review for Calc II by starting from the beginning, and I'm already screwing up problems.
Simple Integration by U-substitution. Here's what I've got so far.

Integral Sec^2(4x+1)dx ; u=4x+1  du=4dx
=(1/4)Int Sec^2(u) du
=(1/4)Tan^2 +1(u)  ??????????

 
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Quote from: BritbongarongLemön on December 06, 2014, 03:34:35 PM
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I have the answer, and that's not it.

 
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Goji, Piranha, Turkey, plz help. I'm surrounded by shitposters.

 
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I[Sec^2(4x+1)]dx ; u=4x+1  du=4dx
I[1/4Sec^2(u)]du
= 1/4(tan(u)) + c

sub back in your u=4x+1

=(1/4)*(tan(4x+1)) + c

sec^2(x) doesn't integrate to tan^2(x) + 1. You might be thinking of tan^2(x) + 1 = sec^2(x)

EDIT: also dont forget your +c
Last Edit: December 06, 2014, 03:48:35 PM by Fedorekd

 
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int(sec^2(4x+1)).dx
u=4x+1
du/dx=4
dx=du*(1/4)

int(sec^2(u)).du*(1/4)
=(1/4)*int(sec^2(u)).du

=(1/4)*(tan(u))+c
=(1/4)*tan(4x+1)+c


The integral of sec^2(u) is tan(u).
Last Edit: December 06, 2014, 03:50:32 PM by Simseo

 
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Nerds

 
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Quote from: Simseo on December 06, 2014, 04:06:08 PM
Quote from: BritbongarongLemön on December 06, 2014, 04:04:36 PM
Nerds
2/cos(c) 4 u
I'm 1/cos(c) and I know it.

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To say, 'nothing is true', is to realize that the foundations of society are fragile, and that we must be the shepherds of our own civilization. To say, 'everything is permitted', is to understand that we are the architects of our actions, and that we must live with their consequences, whether glorious or tragic.
Well, got another one now. Using Washer method, find the volume of the solid when the shaded region is revolved about the X-axis.

y=sqrt(3-x)  y=-1; starts at 3, max height shown is 2
V=int 0|2 pi*([sqrt(3-x)]^2 - [-1]^2)dx
=int 0|2 pi*(3-x-1)dx
=pi*(2-x)^2 /2 0|2

Note: I left in 0|2, although I don't think it's right, because I already tried several other things and nothing has worked so far.

 
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Quote from: The First Noelle on December 06, 2014, 05:05:51 PM
When it comes to math, I am retarded as well.
Just maths? Could've fooled me.

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Quote from: AC on December 06, 2014, 04:56:31 PM
Well, got another one now. Using Washer method, find the volume of the solid when the shaded region is revolved about the X-axis.

y=sqrt(3-x)  y=-1; starts at 3, max height shown is 2
V=int 0|2 pi*([sqrt(3-x)]^2 - [-1]^2)dx
=int 0|2 pi*(3-x-1)dx
=pi*(2-x)^2 /2 0|2

Note: I left in 0|2, although I don't think it's right, because I already tried several other things and nothing has worked so far.
EDIT: Oh shit, I haven't done the washer method. Was doing it a different way.
Last Edit: December 06, 2014, 05:12:55 PM by Fedorekd

 
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"flaming nipple chops"-Your host, the man they call Ghost.

To say, 'nothing is true', is to realize that the foundations of society are fragile, and that we must be the shepherds of our own civilization. To say, 'everything is permitted', is to understand that we are the architects of our actions, and that we must live with their consequences, whether glorious or tragic.
Quote from: Fedorekd on December 06, 2014, 05:10:20 PM
Quote from: AC on December 06, 2014, 04:56:31 PM
Well, got another one now. Using Washer method, find the volume of the solid when the shaded region is revolved about the X-axis.

y=sqrt(3-x)  y=-1; starts at 3, max height shown is 2
V=int 0|2 pi*([sqrt(3-x)]^2 - [-1]^2)dx
=int 0|2 pi*(3-x-1)dx
=pi*(2-x)^2 /2 0|2

Note: I left in 0|2, although I don't think it's right, because I already tried several other things and nothing has worked so far.
EDIT: Oh shit, I haven't done the washer method. Was doing it a different way.
Yeah, the answer is supposed to be 8pi, but I cannot get it no matter what variables I change.

 
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Quote from: AC on December 06, 2014, 04:56:31 PM
Well, got another one now. Using Washer method, find the volume of the solid when the shaded region is revolved about the X-axis.

y=sqrt(3-x)  y=-1; starts at 3, max height shown is 2
V=int 0|2 pi*([sqrt(3-x)]^2 - [-1]^2)dx
=int 0|2 pi*(3-x-1)dx
=pi*(2-x)^2 /2 0|2

Note: I left in 0|2, although I don't think it's right, because I already tried several other things and nothing has worked so far.
protip: DRAW A PICTURE. it makes volumes of rotation soooooo much simpler, and it'll probably help it click.