Lamalam
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An integeation q , anyone can tell me where I did wrong? And also can someone tell when should I use substitution and when should I use integration by parts?
Thank you so much!
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m4ths/maths247
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(Original post by Lamalam)
An integeation q , anyone can tell me where I did wrong? And also can someone tell when should I use substitution and when should I use integration by parts?
Thank you so much!
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You can see there is a relationship between the product with this question. One function is the derivative of the other (or a multiple of it). At this point use substitution of even recognition.
Parts would be more suitable when the product is made up of 2 distinct functions. xlnx has two distinct functions where one is not the derivative of the other (ergo use parts) yet 2x(e^x^2) is a product of a function and it's derivative. Here recognition or substitution would be used.
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Lamalam
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(Original post by m4ths/maths247)
You can see there is a relationship between the product with this question. One function is the derivative of the other (or a multiple of it). At this point use substitution of even recognition.
Parts would be more suitable when the product is made up of 2 distinct functions. xlnx has two distinct functions where one is not the derivative of the other (ergo use parts) yet 2x(e^x^2) is a product of a function and it's derivative. Here recognition or substitution would be used.
What is recognition??
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Anythingoo1
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(Original post by Lamalam)
What is recognition??
When you look at an integral and you can "recognise" what it will integrate into by using the differential
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Lamalam
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(Original post by Anythingoo1)
When you look at an integral and you can "recognise" what it will integrate into by using the differential
Can u helping telling me what mistakes did I make??

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Anythingoo1
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(Original post by Lamalam)
Can u helping telling me what mistakes did I make??

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sure, give me a few mins
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m4ths/maths247
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(Original post by Lamalam)
Can u helping telling me what mistakes did I make??

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Why not just use substitution instead rather than using parts?
It is similar to asking how to use integration by parts for the integral of p x p
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Anythingoo1
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(Original post by Lamalam)
Can u helping telling me what mistakes did I make??

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There are different ways to approach this question, the first that I thought of was not covered in your syllabus (further maths), but upon inspection you can do this quite easily by substitution, exactly what's in the red pen

I don't think by parts is a viable choice for that question, you may be able to do it but it would be much more effort than substitution
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B-Stacks
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(Original post by Lamalam)
An integeation q , anyone can tell me where I did wrong? And also can someone tell when should I use substitution and when should I use integration by parts?
Thank you so much!
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You went wrong in a few places, you seem to lack a bit of understanding on integrals with limits and your working out is not clear enough for me to gather what you are doing.
When you used Integration parts you can see that in the second part you get given the expression from the original question. If you tried to integrate it again by parts you would get them same again and again which would get you nowhere. This shows recognition or substitution must be used.


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goku24
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(Original post by Lamalam)
An integeation q , anyone can tell me where I did wrong? And also can someone tell when should I use substitution and when should I use integration by parts?
Thank you so much!
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Substitution when you have a function and (a multiple of) it's derivative.

By parts when you can't spot an obvious substitution.

You started off wrong, if u is sin(x) and du is cos(x), you should get u^2 du.

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Lamalam
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(Original post by B-Stacks)
You went wrong in a few places, you seem to lack a bit of understanding on integrals with limits and your working out is not clear enough for me to gather what you are doing.
When you used Integration parts you can see that in the second part you get given the expression from the original question. If you tried to integrate it again by parts you would get them same again and again which would get you nowhere. This shows recognition or substitution must be used.


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Because I was taught that if I see the same given expression I can actually move that to the left hand side of the equation. I think I am confused.
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m4ths/maths247
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(Original post by Lamalam)
Because I was taught that if I see the same given expression I can actually move that to the left hand side of the equation. I think I am confused.
But your teacher is not going to tell you to use parts on this integral.
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Lamalam
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(Original post by m4ths/maths247)
But your teacher is not going to tell you to use parts on this integral.

ha yeah
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Dilzo999
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This type of integral should be easily recognisable because you know that the differential of sin(t) is cos(t) so you know you can do this by recognition. People do get confused because it's trig but the same rules apply .
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