(OT) Calculus Help for Morons

[Trevalon Moonleirion]

HEEEEELLLLLP!


My diabolical AP Calc teacher is making us work very hard AFTER all the AP tests are over... it's evil... anyhow... someone, anyone... PLEASE help with with one or both of these problems!


(1.) ç (sin^3 x)(cos^2 x)dx
(Translation if it looks weird on the computer...: integrate sine cubed x times cosine squared x)



(2.) 1ç0 1/ ã(4-x^2)
(Translation: integrate, from zero to one, 1 over the square root of 4 minus x squared)

 

[dexterace]

1) sin^3cos^2=sin(1-cos^2)cos^2= sin*cos^2-sin*cos^4

let u=cos(x) then du=-sin(x)dx

so integral is: -int(u^2du)+int(u^4du)=-u^3/3+u^5/5=-cos^3/3+cos^5/5


2) let x=2sin(u) then dex=2cos(u)du

then integral is: int(dx/sqrt(4-x^2))=int[2cos(u)du/sqrt(4-4sin^2(u))]
=int[cos(u)/sqrt(cos^2(u))]=int(du)=1-0=1

 

[MeepoTheMighty]

1) Rewrite it in terms of sin x: (sin^3 x)(cos^2 x) = (sin^3 x)(1-sin^2 x)

Then let u = sin x so you have (integral) u^3(1-u^2)du. Should be pretty straightforward after that.

2) Ugh...I need to think about this one. I'll get back to you.

 

[dexterace]

Meepo,

Your solution to #1 is incorrect because you forgot that du=cos(x) dx

 

[MeepoTheMighty]

Good point. Ignore my answer then.

 

[Trevalon Moonleirion]

OOOOOH! Answers are good! Me likes getting help from friendly people!



Good lord... look at what calculus does to my brain... i'm talking like i'm 2

Thank you and keep on working if you see problems... god i love this board!

 

[jgbrowning]

It really is an arcane language, isn't it?

joe b.

 

[ergeheilalt]

*drools, eyes begin glazing over*

uh ... goodie! That is what I have to look forward to ...

*begins looking for the rope*

 

[Trevalon Moonleirion]

It really is an arcane language, isn't it?

joe b.

It looks much nicer when you're writing it out instead of typing it on your screen... on the computer you struggle to get your point across... I usually just pretend that I'm using my graphing calculator...

x squared becomes x^2

division becomes /

multiplication is *

ya know... stuff like that...

But for all you know...maybe we're casting spells on you...

 

[jgbrowning]

It looks much nicer when you're writing it out instead of typing it on your screen... on the computer you struggle to get your point across... I usually just pretend that I'm using my graphing calculator...

x squared becomes x^2

division becomes /

multiplication is *

ya know... stuff like that...

But for all you know...maybe we're casting spells on you...

Yes, master.

joe b.