Integration mega collection Watch

tombayes
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#21
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#21
(Original post by TeeEm)
I have that one (by complex or parts), but I will add some powers of sin/cos/tan via complex route as you suggested
have a look:

http://math.mit.edu/~sswatson/pdfs/q...round_2014.pdf
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TeeEm
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#22
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#22
Saved it because that has limits ...

I have several booklets with all sorts and I need to check because there have too many and often I forget what is there.


many thanks.
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Zen-Ali
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#23
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#23
(Original post by Hasufel)
...
To make brackets bigger, put \left( and \right) as opposed (). I.e.:

\left(\dfrac{1}{2}\right)

(Quote it and look at the code.)
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tombayes
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#24
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#24
(Original post by TeeEm)
Saved it because that has limits ...

I have several booklets with all sorts and I need to check because there have too many and often I forget what is there.


many thanks.
integrals with limits allow for so many more tricks . Especially differentiation under the integral sign as used by Feynman...
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TeeEm
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#25
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#25
(Original post by tombayes)
integrals with limits allow for so many more tricks . Especially differentiation under the integral sign as used by Feynman...
Totally agreed

That is why I saved the sheet for later "digestion"

I am a compulsive resource "thief/hoarder"
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TeeEm
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#26
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#26
(Original post by notnek)
My suggestion for a disgusting integral:

\displaystyle \int \frac{1}{(\cos^2 x +4\sin x - 5)\cos x} \ dx

Probably more because of it's length as opposed to its difficulty.


This was a beautiful ugly integral !!

(it will be added when I next update my booklets in around 30 days)

many thanks

Spoiler:
Show


it even generated offspring/ look at page 2 (ignore the induction at the top half)

I hope there are no mistakes

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TeeEm
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#27
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#27
(Original post by Hasufel)
this one looks simple (i dare ya!):

\displaystyle \int \frac{\sin(x)}{1-\tan(x)}dx

(equivalent to \displaystyle \int \frac{\sin(x)\cos(x)}{\cos(x)-\sin(x)}dx )
this integral was "marriage material"!!
It will be added in the next update of the booklet at the end of November.

This is my method, I hope I made no mistakes.
If there is a clever alternative give me hint.

Thanks

Spoiler:
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TeeEm
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#28
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#28
(Original post by TeeEm)
I am attaching in this thread an integration booklet with 622 indefinite integrals at present ( 5 new ones to be added shortly)

This is the student version of the booklet which has no answers or solutions.
(A carbon copy of this document with answers and full solutions also exists but it is too large to attach here)

Can you suggest any decent "beautifully disgusting" integrals to add to this collection.
Indefinite integrals only please.
(undergrad techniques are ok, within reasonable difficulty)


Attachment 334657


The booklet is not in strict "hardness" order but overall the questions get progressively harder

Many thanks

Note that at Q350 onwards a large proportion of integrals will be only accessible to further mathematicians

UPDATED FILE

integration_indefinite_mixed_up_student_version_condense.pdf


I have just added the five new questions contributed making the total 627

New questions are 406 - 410

[The solution version booklet in my site will be updated early next week]
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TeeEm
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#29
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#29
UPDATED FILE


integration_indefinite_mixed_up_student_version_condense.pdf

I have just added quite a few new questions contributed making the total 668.
I also changed the order a bit, particularly at the start.

happy integration


[The solution version booklet is approximately 60 Mb and it will not upload here, so it is only available in my site ]


PS Mr M got a mention in the solution of Q 666
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Phichi
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#30
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#30
I'm so sad, you should make an exception to the indefinite only to include:

\int_{-\infty}^{\infty} e^{-x^2} \,dx

Shame, it's beautiful
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TeeEm
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#31
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#31
(Original post by Phichi)
I'm so sad, you should make an exception to the indefinite only to include:

\int_{-\infty}^{\infty} e^{-x^2} \,dx

Shame, it's beautiful
Perhaps a bit too advanced for A level maths or further maths
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Phichi
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#32
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#32
(Original post by TeeEm)
Perhaps a bit too advanced for A level maths or further maths
I'd say it's easier than a lot of them in the collection, just a conversion to polar co-ordinates, I could do it at A-Level
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Kvothe the Arcane
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#33
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#33
Great resource. Will use .

(Original post by Phichi)
I'd say it's easier than a lot of them in the collection, just a conversion to polar co-ordinates, I could do it at A-Level
Only one I've done in TPIT thread.
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