Recent content by Bill333

Thank you for your replies; the question stipulated not to find the determinant directly, and gave a hint concerning the interchanging of rows and columns; I presumed that it did not mean use addition of rows and columns. Fightfish, to clarify, are you saying it is impossible to complete using...

Homework Statement Hi there, I'm happy with the proof that any odd ordered matrix's determinant is equal to zero. However, I am failing to see how it can be done specifically for a 3x3 matrix using only row and column interchanging. Homework Equations I have attached the determinant as an...

Ah, thank you very much LCKurtz!

Hi! :) A volume fraction of the cylinder, apologies; the shaded volume, not the shaded area!

Homework Statement Hi ! :) I'm having some difficulties with the question below, in which there are numerous steps and I am unsure in which part(/s!) I have gone wrong. The question is as below; you must via integration calculate the shaded volume of a perfect cylinder of radius R and height...

Ah, is the substitution instead ez = 1/x, thus -(x)-2 dx = ezdz, thus -1/x dx = dz. The integral is now ∫(-1/(x2-1)-0.5*x) dx from 1 to 0, which can be re-written as ∫x/(x2-1)0.5*x) from 0 to 1, which then cancels to give the form as required. Thank you very much for your help, I feel irked...

Homework Statement Show by appropiate substitutions that ∫ (e2z-1)-0.5 dz from 0 to infinity is equivalent to ∫(1-x2)-0.5 dx from 0 to 1. Thus, show that the answer is π/2. Homework EquationsThe Attempt at a Solution Where to begin! I tried the substitution e2z= 2-x2, but this then transforms...