velaris08
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If anyone could help me out with this - attached the sol bank answer below, the q is to find the exact value of f(x) using substitution and give the answer in form 2^q * p. I used the substitution u = sqrt(2-x) - attaching my working below too. Can someone show me where I've got wrong?
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mqb2766
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Did you change the limits?
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MatureLikeManure
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(Original post by mqb2766)
Did you changed the limits?
thats because the limit does not exist
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Muttley79
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(Original post by velaris08)
If anyone could help me out with this - attached the sol bank answer below, the q is to find the exact value of f(x) using substitution and give the answer in form 2^q * p. I used the substitution u = sqrt(2-x) - attaching my working below too. Can someone show me where I've got wrong?
Can you post what you did?
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davros
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(Original post by velaris08)
If anyone could help me out with this - attached the sol bank answer below, the q is to find the exact value of f(x) using substitution and give the answer in form 2^q * p. I used the substitution u = sqrt(2-x) - attaching my working below too. Can someone show me where I've got wrong?
as per above suggestion, it doesn't look like you've changed your x limits into equivalent u limits
(Original post by MatureLikeManure)
thats because the limit does not exist
That doesn't make sense, unless you're trying to make a joke?
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velaris08
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(Original post by mqb2766)
Did you change the limits?
Don’t get why I’d need to? I know the answer does but I can’t lie, don’t get why they did…
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mqb2766
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(Original post by velaris08)
Don’t get why I’d need to? I know the answer does but I can’t lie, don’t get why they did…
Youve transformed the integration variable from x to u. The original limits are in terms of x, you need to transform them as well to represent the corresponding values of u. It should be in your book?

If you notice, in the model solution the limits change from 0->2 to 2->0. This is because of the transformation
u = 2-x
The integration problem is now in terms of u, not x. See the pic at the top of
https://infinityisreallybig.com/2020...f-integration/
The integration (upper) limit is transformed.
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velaris08
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(Original post by mqb2766)
Youve transformed the integration variable from x to u. The original limits are in terms of x, you need to transform them as well to represent the corresponding values of u. It should be in your book?

If you notice, in the model solution the limits change from 0->2 to 2->0. This is because of the transformation
u = 2-x
The integration problem is now in terms of u, not x. See the pic at the top of
https://infinityisreallybig.com/2020...f-integration/
The integration (upper) limit is transformed.
Oh - I thought that we just do that for when we find the area under a curve with parametric equations, not in general? But now I'm looking back - yeah they do say to do that. I remember for the earlier ones with u I was thinking that if u = x then surely we should change the limits as well and then realised that since they're equal the limits are the same and I guess I digested the "equal" more than I did "in this case". Thanks lol.
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