# Integration

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#2

(Original post by

If i was integrating using substitution of , would i need to change the values of 2 and 0 or not?

Since i replace u at the end anyway?

Thanks!

**Zenarthra**)If i was integrating using substitution of , would i need to change the values of 2 and 0 or not?

Since i replace u at the end anyway?

Thanks!

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#3

**Zenarthra**)

If i was integrating using substitution of , would i need to change the values of 2 and 0 or not?

Since i replace u at the end anyway?

Thanks!

Secondly, when you make a substitution you have to keep everything consistent - either write your final result as a function of u and change your limits to u limits, or convert your final result back into a function of x and use the original x limits.

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#4

**Zenarthra**)

If i was integrating using substitution of , would i need to change the values of 2 and 0 or not?

Since i replace u at the end anyway?

Thanks!

The minute your function includes any u your limits should read x=

__My practice is to__

Write limits as values

Introduce u and change limits to x=

(if sticking with u)Change limits to u=

Then continue with values

(if planning n a return to x)Continue with x=

Only return to numbers after the re-substitution

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(Original post by

I would agree with Davros (I have been doing that a lot lately) but would go further and take usycool's point

The minute your function includes any u your limits should read x=

Write limits as values

Introduce u and change limits to x=

(if sticking with u)Change limits to u=

Then continue with values

(if planning n a return to x)Continue with x=

Only return to numbers after the re-substitution

**TenOfThem**)I would agree with Davros (I have been doing that a lot lately) but would go further and take usycool's point

The minute your function includes any u your limits should read x=

__My practice is to__Write limits as values

Introduce u and change limits to x=

(if sticking with u)Change limits to u=

Then continue with values

(if planning n a return to x)Continue with x=

Only return to numbers after the re-substitution

(Original post by

Firstly, I don't think you wrote what you meant to - I presume your integral should be of a square root, not the x-th root as you've written it.

Secondly, when you make a substitution you have to keep everything consistent - either write your final result as a function of u and change your limits to u limits, or convert your final result back into a function of x and use the original x limits.

**davros**)Firstly, I don't think you wrote what you meant to - I presume your integral should be of a square root, not the x-th root as you've written it.

Secondly, when you make a substitution you have to keep everything consistent - either write your final result as a function of u and change your limits to u limits, or convert your final result back into a function of x and use the original x limits.

And also TenOfThem thanks, but would be easier when you have limits in x, change them to u and just substitute the limits into u when integrated?

Would I get the same answer?

ThankS!

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#6

(Original post by

Yes you're right davros, i didnt mean to write it out like that. It's my first time using latex so forgive me.

And also TenOfThem thanks, but would be easier when you have limits in x, change them to u and just substitute the limits into u when integrated, so it would say replacing u?

I said get the same answer right?

ThankS!

**Zenarthra**)Yes you're right davros, i didnt mean to write it out like that. It's my first time using latex so forgive me.

And also TenOfThem thanks, but would be easier when you have limits in x, change them to u and just substitute the limits into u when integrated, so it would say replacing u?

I said get the same answer right?

ThankS!

"By making the substitution we have ... "

I see a lot of books trying to be "clever" by saying things like "Let ...", but this hides the subtlety that you have a choice of which square root to take when you change the limits.

You can write or and get the correct answer either way, but it makes it explicit what you're doing when you convert the limits!

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(Original post by

If you replace it, no, but probably best to make it clear that x = 2 or x = 0 (as opposed to u) in the limits.

**usycool1**)If you replace it, no, but probably best to make it clear that x = 2 or x = 0 (as opposed to u) in the limits.

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(Original post by

Personally, I would go even further and write u explicitly as a function of x like this:

"By making the substitution we have ... "

I see a lot of books trying to be "clever" by saying things like "Let ...", but this hides the subtlety that you have a choice of which square root to take when you change the limits.

You can write or and get the correct answer either way, but it makes it explicit what you're doing when you convert the limits!

**davros**)Personally, I would go even further and write u explicitly as a function of x like this:

"By making the substitution we have ... "

I see a lot of books trying to be "clever" by saying things like "Let ...", but this hides the subtlety that you have a choice of which square root to take when you change the limits.

You can write or and get the correct answer either way, but it makes it explicit what you're doing when you convert the limits!

Would i replace the u's or just get the u's from the x values and find the area that way, would it give me the same answer?

ThankS!

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#9

(Original post by

...

**Zenarthra**)...

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#10

Also how would you go about solving the intagral in the OP? Is it possible to do with a-level (including fm) knowledge? Is it even possible to find the closed form of the integral?

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#11

(Original post by

Also how would you go about solving the intagral in the OP? Is it possible to do with a-level (including fm) knowledge? Is it even possible to find the closed form of the integral?

**JerzyDudek**)Also how would you go about solving the intagral in the OP? Is it possible to do with a-level (including fm) knowledge? Is it even possible to find the closed form of the integral?

Actually, looking at the OP's last post I think I'd assumed that x wasn't supposed to be there at all whereas in fact I think the OP intended it to be outside the root and multiplying it, but I don't think that changes any of the arguments above - either the root on its own or the root multiplied by x can be integrated.

OP: if you let then when you change to an integral in u, the limits must be changed too:

x = 0 =>

x = 2 => u = 3

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#12

**JerzyDudek**)

Also how would you go about solving the intagral in the OP? Is it possible to do with a-level (including fm) knowledge? Is it even possible to find the closed form of the integral?

edit: impossible to do as its impossible to get it all in terms of 1 variable with A-level knowledge(i think) therefore limits cant be applied

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(Original post by

If you mean the one that appeared to have an x-th root in it, then no, I don't think there's a closed form for it!

Actually, looking at the OP's last post I think I'd assumed that x wasn't supposed to be there at all whereas in fact I think the OP intended it to be outside the root and multiplying it, but I don't think that changes any of the arguments above - either the root on its own or the root multiplied by x can be integrated.

OP: if you let then when you change to an integral in u, the limits must be changed too:

x = 0 =>

x = 2 => u = 3

**davros**)If you mean the one that appeared to have an x-th root in it, then no, I don't think there's a closed form for it!

Actually, looking at the OP's last post I think I'd assumed that x wasn't supposed to be there at all whereas in fact I think the OP intended it to be outside the root and multiplying it, but I don't think that changes any of the arguments above - either the root on its own or the root multiplied by x can be integrated.

OP: if you let then when you change to an integral in u, the limits must be changed too:

x = 0 =>

x = 2 => u = 3

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(Original post by

When you make a change of variable, you must change the limits to your new variable. When you revert back to your original variable, revert your limits back to normal.

**Khallil**)When you make a change of variable, you must change the limits to your new variable. When you revert back to your original variable, revert your limits back to normal.

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#15

(Original post by

Sorry im a little confused here's what i mean:

Would i replace the u's or just get the u's from the x values and find the area that way, would it give me the same answer?

ThankS!

**Zenarthra**)Sorry im a little confused here's what i mean:

Would i replace the u's or just get the u's from the x values and find the area that way, would it give me the same answer?

ThankS!

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