Halloween and Calculus

[Goistein]

I have only one day left to make my costume as Mr. Calculus. On the costume, I'm putting every derivative law and integral law I know. But I can't get the anti-derivative of x^x. Please help!

 

[stapel]

I have only one day left to make my costume as Mr. Calculus. On the costume, I'm putting every derivative law and integral law I know. But I can't get the anti-derivative of x^x. Please help!

You say you're decorating with every integral you know. Since this is an integral that can't be done, then... can't you leave it off...?

Eliz.

 

[Goistein]

OK, but I'm also looking for anti-derivatives of inverse trig functions. (All 6).

 

[Denis]

http://www.geocities.com/pkving4math2to ... g_func.htm


Halloween favorite dessert: BOOberry pie and I SCREAM :roll:

 

[jwpaine]

http://www.geocities.com/pkving4math2tor4/4_the_elem_transc_func/4_01_02_02_diffn_of_the_inv_trig_func.htm


Halloween favorite dessert: BOOberry pie and I SCREAM :roll:

All images on that page have invalid links - aka: broken

 

[galactus]

Here they are:

http://www.efunda.com/math/derivatives/TrigD.cfm

 

[Deleted member 4993]

I think he was looking for "anti-derivatives" of the inverse-trig function.

That would be a good excercize for Mr. Calculus.

Hint:

[integral]sin^(-1)(x) dx

= x * sin[sup]-1[/sup]x - [integral][x/{sqrt(1-x^2})] dx

Now continue....

 

[galactus]

Any good calc texts has these in the cover.

\(\displaystyle \L\\\int{csc^{-1}(u)}du=ucsc^{-1}(u)du+ln|u+\sqrt{u^{2}-1}|+C\)

\(\displaystyle \L\\\int{sec^{-1}(u)}du=usec^{-1}(u)-ln|u+\sqrt{u^{2}-1}|+C\)

\(\displaystyle \L\\\int{cot^{-1}(u)}du=ucot^{-1}(u)+ln\sqrt{1+u^{2}}+C\)

\(\displaystyle \L\\\int{tan^{-1}(u)du}=utan^{-1}(u)-ln\sqrt{1+u^{2}}+C\)

\(\displaystyle \L\\\int{cos^{-1}(u)}du=ucos^{-1}(u)-\sqrt{1-u^{2}}+C\)

\(\displaystyle \L\\\int{sin^{-1}(u)}du=usin^{-1}(u)+\sqrt{1-u^{2}}+C\)