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# Integration question on core 3 January 2013 paper

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1. Is the mark scheme right? I thought you would have to do integration by parts, but it's as if the mark scheme has just forgot about the x next to it. Am I missing something really simple here?
2. This is the question.
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3. Let u=( X^2 + 3)^ 1/2
then dx= udu/x on substitution u get the answer
4. The attached solution is incorrect
5. (Original post by gonza nelson)
Let u=( X^2 + 3)^ 1/2
then dx= udu/x on substitution u get the answer
so can you not do it by parts?
6. (Original post by gonza nelson)
The attached solution is incorrect
No it's not.
7. (Original post by lucyjane_x)
so can you not do it by parts?
No. Using parts would make it much more complicated and go beyond A Level.

Either you can use recognition by considering the derivative of sqrt(x^2+3). This is the method the mark scheme has used.

You should be spotting that x is close to the derivative of x^2+3 so recognition can be used. I'm not sure how you've been taught in school but this method makes these kind of integrals much faster,

Or use substitution - I would substitute u^2=x^2+3. But u=x^2+3 works also.
8. (Original post by lucyjane_x)
so can you not do it by parts?
I can see why you thought of using parts here. The reason why it wouldn't be useful is because parts would get rid of the 'x' and leave you with an integral of sqrt(x^2+3). But this is not an easy integral.
9. (Original post by lucyjane_x)
Is the mark scheme right? I thought you would have to do integration by parts, but it's as if the mark scheme has just forgot about the x next to it. Am I missing something really simple here?
Let u = x^2 + 3.
10. (Original post by TheLifelessRobot)
Let u = x^2 + 3.
Your final answer??
11. (Original post by gonza nelson)
Your final answer??
I get the same answer as the one listed in the mark scheme

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