Is this a typo? - Integral of fraction

[anthonyk2013]

Part (1) of this question posted in post 3. Is it a type-o or correct. Not looking for solution.

 

[Doug Huffman]

Yes, it appears to be so, from what I can see.

 

[anthonyk2013]

 

[anthonyk2013]

Forgot the image

 

[DarthMatter]

What is a type-o? Or do you think it is a typo? Then type-o probably is a typo.
The integrals look ok so far.

 

[DarthMatter]

Hint for part i): Try to rearrange $6x^2-5x+3$ into some polynome your can divide by $12x-5$ plus a constant.

 

[anthonyk2013]

Ya I differentiated the top and you get 12x-5 all over 12x-5.

 

[DarthMatter]

Ah I see. Could be a typo. But this integral should be solvable as well.

 

[anthonyk2013]

Part 1&2 only worth 4% on exam paper. Seem like a but of work for 2%

 

[DarthMatter]

Part 1&2 only worth 4% on exam paper. Seem like a but of work for 2%

Private theories are not allowed in this forum. :D But don't worry here. Sorry, I can only look at the math.

 

[Mark44]

Anthonyk, why would you think the problem has a typo? This is an easy integral - just divide the numerator by the denominator.

 

[anthonyk2013]

Lecturer thinks it is because of the low mark. Looking back a previous exam papers made an assumption. If We are wrong I hold my hand up.

 

[anthonyk2013]

Anthonyk, why would you think the problem has a typo? This is an easy integral - just divide the numerator by the denominator.

That's are far as I got I had x-1.

 

[Mark44]

That's are far as I got I had x-1.

Well, that's wrong. The first term in the quotient should by (1/2)x. See http://en.wikipedia.org/wiki/Polynomial_long_division.

 

[anthonyk2013]

Ya silly mistake by me.

 

[anthonyk2013]

Wondering the the solution the this question is right or wrong ?
Thanks

 

[mfb]

What happened in (4)? The denominators vanished?
Also, what happens if you differentiate your result? Do you get the initial fraction? This is often a very easy check you can always do if you are unsure.

The whole substitution is not helpful here. Posts 6 and 11 show the best approach.

 

[anthonyk2013]

This solution is from class. We were given a reason why that were moved but I can remember.
When studying on my own I divided the polynomial but the devision didn't look right. I'll attempt it again and post later. Thanks.

 

[anthonyk2013]

 

[mfb]

Looks right so far.

 

[Mark44]

@anthonyk2013, once you've made it past grade school arithmetic, it's not a good idea to write fractions as mixed numbers (such as you have in your work). Instead of $1 \frac 1 {24}$ or $1 \frac {23} {24}$, you really should write these as improper fractions, 25/24 and 47/24. Mixed numbers such as the ones you wrote are much harder to work with and can easily be confused if not written very carefully.

 

[anthonyk2013]

Ill finish later. Too many kids around[emoji86]

 

[anthonyk2013]

Thanks for the reminder mark44. Long time since i was in grade school as you call it

 

[anthonyk2013]

Latest attempt. Wondered if I'm right.

 

[mfb]

Integrating x/2 gave x²/2?
And check what you have in the denominators and logs - but I guess those are just typos.

 

[anthonyk2013]

Should be X²/4