integration/diff extension

[Martoman]

So i'm doing spech now and am finding integration pitiful. 8-) Are there any "good" integral or diff questions at the specialist level that some can recommend? I want things that can make me think or require some cool observations to be made in substitution/linear substitution or anything else. Thanks all!

Edit: there are some really cool ones in the super-happy-fun-maths time but any textbook or other resources?

[/0]

TT had this old spesh book by Fitzpatrick which he said was pretty good for integration.

Alternatively pick up any First year university text. Stewart is pretty good http://rapidshare.com/files/382937087/Calculus_Early_Transcendentals_6th_Edition__Stewart_Series.pdf.html. Just flip to the integration chapter there are a heap of exercises.

There are some here: http://www.mathisfunforum.com/viewtopic.php?id=4208

[Martoman]

HOW ON EARTH DO YOU SOLVE THIS?

I've tried adding +ve and -ve to the top but that does nothing.

[/0]

Mathematica can't even integrate it :/
Perhaps it's not analytically solvable

[Martoman]

Yeah that's what wolfram said.... but its on that site you gave me!!!!

[/0]

Lol.. err nvm that website, the Stewart textbook has some very good exercises

[kyzoo]

So i'm doing spech now and am finding integration pitiful. 8-) Are there any "good" integral or diff questions at the specialist level that some can recommend? I want things that can make me think or require some cool observations to be made in substitution/linear substitution or anything else. Thanks all!

Edit: there are some really cool ones in the super-happy-fun-maths time but any textbook or other resources?

Find the antiderivative of cosec x and sec x

[TrueTears]

yup like /0 said, stewarts is frigging awesome for integration... some are out of VCE course.

the fitzpatrick book was very old but very good, had heaps of good exercises but the explanations were shit

[iffets12345]

my teacher has fitzpatrick, i absolutely cannot find it anywhere! It's green, right?

[tram]

So i'm doing spech now and am finding integration pitiful. 8-) Are there any "good" integral or diff questions at the specialist level that some can recommend? I want things that can make me think or require some cool observations to be made in substitution/linear substitution or anything else. Thanks all!

Edit: there are some really cool ones in the super-happy-fun-maths time but any textbook or other resources?

Find the antiderivative of cosec x and sec x

yea, that is an awesome question kyzoo, lol, i wonder where you got it from.........

[TrueTears]

Find the antiderivative of cosec x and sec x

Using integration of parts (multiple times) to derive the reduction for the integral of sin, we yield:



The explicit form for sin^n(x) would mean a restriction placed on n, so implicitly in this form, it is much more useful.

The rest is trivial for the integral of cosec

An exericse for you, can you try the same deviation to find the reduction for cosine? Then perhaps evaluate the integral of sec

[/0]

Another way:



Another way:

[Martoman]

Another way:



Another way:

The cosec one is perhaps the biggest leap of faith I have ever seen. :S

[TrueTears]

Another way:



Another way:

The cosec one is perhaps the biggest leap of faith I have ever seen. :S

it was how they did it in stewarts

one could do the same for sec too, very similar, apply the same train of thought.

[/0]

Another way:



Another way:

The cosec one is perhaps the biggest leap of faith I have ever seen. :S

That's what I think too. I don't know why it's so standard - 90% of textbooks give that solution.