Evaluating the integral, correct?

[rocomath]

idk w/o working it out or trying to work it out i know you'll want to get [integral] cos^2 x cos x sinx

Nope!

 

[rocomath]

What is the derivative of ...

$$\frac{d}{dx}(\cos^{4}x)$$

?

 

[Zack88]

-4sin^3?

 

[rocomath]

4cos^3?

You forgot the chain rule!

Review your differentiating methods, it'll pay off in being able to recognize some Integrals.

 

[Zack88]

-4sin^3?

 

[rocomath]

-4sin^3?

You forgot the chain rule!

Review your differentiating methods, it'll pay off in being able to recognize some Integrals.

 

[Zack88]

-4sin x cos^3 x

 

[rocomath]

-4sin x cos^3 x

Yes!

$$-4\cos^{3}x\sin x$$

Now go back to that Integral I asked you about. It's just the chain-rule in "reverse".

 

[Zack88]

$$\int \cos^{3}x\sin x dx$$

- cos^4 x / 4

 

[rocomath]

-4sin^3?

$$\int \cos^{3}x\sin x dx$$

- cos^4 x / 4

Yep. Now look at this problem, but don't pay attention the first part, the 2nd step is what I'm mainly talking about. I spent like an hour evaluating it through Parts a couple times, till I got tired and asked for helped and look how simple it was ...

http://alt1.mathlinks.ro/Forum/latexrender/pictures/7/0/6/70647ef6282a942aac0b3d590d940f1bd06e16d3.gif

 

[Zack88]

I see how you got to step 3 but not to 4

 

[rocomath]

I see how you got to step 3 but not to 4

Oh, don't worry about that. I only wanted to emphasize the chain-rule. Step 3 to 4 would take me forever to type, lol.

I simplified a lot to save myself typing-time. I basically used a trig identity.

 

[Zack88]

lol i was looking at it and then i tilted my head and was like yep i don't know how that happened

 

[Zack88]

woo now i know 6 out of the 18 problems i have to do are correct thanks to you

 

[rocomath]

woo now i know 6 out of the 18 problems i have to do are correct thanks to you

I'm getting sleepy, if you want to do a couple more better start asking :-]

 

[Zack88]

me too me too

[integral] sec^6 x dx

should i do

[integral] (sec^2)^3

or

start doing parts

u= sec^2 x dv = sec^4 x

 

[rocomath]

$$\int\sec^6 xdx$$

$$\int\sec^4 x \sec^2 x dx$$

$$\int(\sec^2 x)^2 \sec^2 xdx$$

When you trig identities raised to powers, break it up till you see something.

 

[Zack88]

[integral] (tan^2 x +1) sec^2 x dx

u = tan x
du = sec^2 x

[integral] (u^2 =1)^2 du

[integral]u^4 + 2u^2 + 1 du

tan^5 x / 5 + 2tan^3 x / 3 + tan x + c

 

[rocomath]

[integral] (tan^2 x +1) sec^2 x dx

u = tan x
du = sec^2 x

[integral] (u^2 =1)^2 du

[integral]u^4 + 2u^2 + 1 du

tan^5 x / 5 + 2tan^3 x / 3 + tan x + c

Good!

 

[Zack88]

woot lol

 

[Zack88]

im goin to let my brain cool down for the night, t2ul and have a good night.

 

[rocomath]

woot lol

Alright, I'm going to sleep! You still have Sunday and Monday to finish all 18 problems!

 

[Zack88]

woo I am back, v.v

[integral] sin^5 x cos^3 x

i was wanting to know if i should break it up like

[integral] sin^4 x sin x cos^2 x cos x

 

[rocomath]

Look in your book, there should be a suggestion on how to tackle even/odd powers of sines and cosines.

Hint: Leave sin^5 x alone, mess around with cos^3 x

 

[Zack88]

[integral] sin^5 x cos^2 x cos x
[integral] sin^5 x (1- sin^2x) cos x

u= sin
du= cos

[integral] u^5(1- u^2) du
[integral] u^5 - u^7 du

1/6 sin^6 x - 1/8 sin^8 x + c

 

[rocomath]

[integral] sin^5 x cos^2 x cos x
sin^5 x (1- sin^2x) cos x
u= sin
du= cos

[integral] u^5(1- u^2) du
u^5 - u^7 du

1/6 sin^6 x - 1/8 sin^8 x + c

Good!

 

[Zack88]

woo, for

[integral] x cos^2 x dx

do i want to use

cos^2 x = (1 + cos^2 x) / 2, then parts

or

[integral] x (1-sin^2x), then parts?

 

[rocomath]

woo, for

[integral] x cos^2 x dx

do i want to use

cos^2 x = (1 + cos^2 x) / 2, then parts

or

[integral] x (1-sin^2x), then parts?

Try a method! Come test day, you got to just go at it :-] You've handled harder problems than this, I'm sure you can do this with ease.

 

[Zack88]

sorry had a fire drill and then went to go eat

im goin to do the (cos^2 x)/ 2 and then the chain rule

 

[Zack88]

[integral] x cox^2 x dx

u= x
du = dx

dv= cos^2
v= (sin(2x)) / 4 + x/2

x (sin(2x)) / 4 + x/2 - [integral] (sin(2x)) / 4 + x/2 du

x (sin(2x)) / 4 + x/2 + cos(2x) / 8 + x^2 / 4 + c