Integration Q

That's why I'm confused. The exercise I'm doing ONLY concerns the 2 methods I mentioned right at the beginning of the post.

Posted from TSR Mobile

Both of those that you mentioned arevspecific cases of the inverse chain rule

Reply 21

ps1265A

OP

14

Original post by TenOfThem

Both of those that you mentioned arevspecific cases of the inverse chain rule

And I cannot use either of them for this Q? Having tried both, my answer would be no

Posted from TSR Mobile

Reply 22

username1560589

20

Original post by ps1265A

And I cannot use either of them for this Q? Having tried both, my answer would be no

Posted from TSR Mobile

If in doubt, use the general formulation of inverse chain rule:

\int f(x)dx = \int f(x)\frac{dx}{du}du

Reply 23

TenOfThem

18

Original post by ps1265A

And I cannot use either of them for this Q? Having tried both, my answer would be no

Posted from TSR Mobile

No ... Since they are specific rules that only apply to specific cases

Are they not presented as specific cases in your textbook? It seems odd that the book is just presenting them without the general context.

Reply 24

Goods

16

Original post by ps1265A

Integrate xe^x^2

So I am going to use the rule f'(x)/f(x) ... However it's not a fraction, can I still apply it here?

Posted from TSR Mobile

the derivative of e^f(x) is f'(x)e^f(x).
therefore the derivative of e^x^2 is 2xe^x^2.
integration is the inverse of differentiation... [ you do some maths] ... Ta da an answer!

Reply 25

davros

16

Original post by ps1265A

And I cannot use either of them for this Q? Having tried both, my answer would be no

Posted from TSR Mobile

As TenOfThem says, you're trying to remember lots of specific rules when you should be looking at the general principle of what's going on.

Try differentiating

e^{x^2}

and compare with the answer you're trying to get.

Next try differentiating

e^{f(x)}

for various functions f(x) and see what form the answers come out in.

Reply 26

AG Singh

3

put it in the form you want, you know you're looking for f'(x)e^f(x) so write that integral out and say to yourself 'what constant do i need to pull out to make my new integral look like my old one' it's not a tricky question :smile:

Reply 27

ps1265A

OP

14

Original post by TenOfThem

No ... Since they are specific rules that only apply to specific cases

Are they not presented as specific cases in your textbook? It seems odd that the book is just presenting them without the general context.

The book has simply stated the 2 rules. And there is an exercise of questions in which you use the rules. That's why I'm confused because one of the rules is supposed to work apparently.

Posted from TSR Mobile

Reply 28

ps1265A

OP

14

Original post by davros

As TenOfThem says, you're trying to remember lots of specific rules when you should be looking at the general principle of what's going on.

Try differentiating

e^{x^2}

and compare with the answer you're trying to get.

Next try differentiating

e^{f(x)}

for various functions f(x) and see what form the answers come out in.

I know how to get to the answer using different integration techniques. But my concern is whether or not the answer can be brought by inspection, but it seems as it cannot.

Posted from TSR Mobile

Reply 29

TenOfThem

18

Original post by ps1265A

The book has simply stated the 2 rules. And there is an exercise of questions in which you use the rules. That's why I'm confused because one of the rules is supposed to work apparently.

Posted from TSR Mobile

Original post by ps1265A

I know how to get to the answer using different integration techniques. But my concern is whether or not the answer can be brought by inspection, but it seems as it cannot.

Posted from TSR Mobile

It does not use either of those rules

But

It is just by inspection

Those 2 are specific cases of "by inspection"

Reply 30

davros

16

Original post by ps1265A

I know how to get to the answer using different integration techniques. But my concern is whether or not the answer can be brought by inspection, but it seems as it cannot.

Posted from TSR Mobile

You can get the answer by 'inspection' BUT 'inspection' isn't some magic method that produces the answer out of nowhere - it's the result of understanding how the derivative of various composite functions looks and it comes with experience and practice :smile:

Reply 31

ps1265A

OP

14

Original post by davros

You can get the answer by 'inspection' BUT 'inspection' isn't some magic method that produces the answer out of nowhere - it's the result of understanding how the derivative of various composite functions looks and it comes with experience and practice :smile:

Ah okay thanks! I've come across another Q in that same exercise: y = e^sinx

This is my method:
ImageUploadedByStudent Room1421778410.828030.jpg

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Reply 32

TenOfThem

18

Original post by ps1265A

Ah okay thanks! I've come across another Q in that same exercise: y = e^sinx

This is my method:
ImageUploadedByStudent Room1421778410.828030.jpg

Posted from TSR Mobile

That is totally incorrect

When you differentiate or integrate e^f(x) you do not introduce powers

The differential of e^sinx is cosx e^sinx by the chain rule

Reply 33

AG Singh

3

did you get to the answer of your original question which was- (1/2e^(x^2) +c)?

Integration Q

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