integation (1 Viewer)

[sukiyaki]

how would we do d) and f)

thanks in advance

 

[George W. Bush]

d is basically the same question as e....


for f, d(logx^2)/dx = 1/2x.

So integrate 1/2 * (log x^2)/2x...

 

[CM_Tutor]

(f) is using log laws then a u = ln x substitution.

I'll give the others some thought, and post later tonight if the question remains unanswered.

 

[:: ck ::]

[d] and [e] : expand out the odd trigonometric functions then use u substitution ..

[f] .. rewrite as : 2 * integral [1/x * logx] (log laws)
u have fn and its derivative .. so indef integral is [logx]^2 + C [use u substitution to verify]

 

[mojako]

Originally posted by George W. Bush
d is basically the same question as e....


for f, d(logx^2)/dx = 1/2x.

No. See other posts.

Originally posted by :: ryan.cck ::
[d] and [e] : expand out the odd trigonometric functions then use u substitution ..

What do you mean by expand out?
In Extension 2 you would write the odd thing like this:
sin^3(x) = sin(x) * sin^2(x)
= sin(x) * [1 - cos^2(x)]
So now you can let u = cos(x) and then du/dx is -sin(x), and since there's only 1 sin(x) left so it's easy to integrate.

 

[CM_Tutor]

Originally posted by mojako
What do you mean by expand out?

FWIW, I took ryan to mean the method that you are describing.

 

[:: ck ::]

that is wot i meant mojako