Further properties of definite integrals (1 Viewer)

[WEMG]

I'm completely lost in definite integrals for 4u integration. The textbook is not making any sense to me. The Cambridge textbook is just confusing and the Terry Lee one just gives one single example with no explanations at all.

Could someone kind enough please explain to me briefly the idea of this method/topic or provide me with some notes etc.

Thanks

EDIT: BTW, is 'Further Properties of Definite Integrals' in the syllabus?

 

[iSplicer]

You could perhaps start by presenting a sample question.

 

[nrlwinner]

Is this the f(x) = f(x-a) and the odd/even stuff?

 

[WEMG]

Yes it is....

 

[Bored Of Fail 2]

come on man, thats all easy

 

[WEMG]

Can u explain it to me?


In this example, how did it get from line 1 to line 2? I know how he got (u^2)/(e^-u+1) to (u^2.e^u)/(1+e^u) but what happened to the (-du) and how did he change -2 and 2 to 2 and -2

 

[Bored Of Fail 2]

lol thats just standard 2unit property int f(x) dx [ from a ..b ] = - int f(x) dx [ from b..a ]

 

[WEMG]

Lol..... Yep...... Okay thanks got it now

 

[Bored Of Fail 2]

when you swap the order of the limits you introduce a negative , this is because instead of your dx being a positive value ( which it is if you go from lowest value to highest value ) , it is a negative value , and think of integration as summing up areas of little rectangles and it is the sum of f(x) dx over the limits


ie the rectangle has height "f(x)" and width "dx" , if dx is negative it is obvious the integral will be negative