Property of Integration :: Please confirm it

[Communications_Engineer]

Hi all,

please confirm for me the property of integration. I'm confused.

 

[albbg]

No. They aren't.

about the first one we can write: ∫10•x•dx=10•∫x•dx

but ∫xdx=x²/2

then the solution of the first one is:
10•(b²/2 - a²/2)

and the second one is:

(10•b)²/2 - (10•a)²/2 = 100•(b²/2 - a²/2)

 

[MANILKA]

I think you have got the answer from @albbg. However, his explanation is based on numerical values. If you are not satisfied with it, the best way to think about it is by using the Riemann integral where the Riemann sphere and the sets are defined. You may find a broad study of this matter in Real & Complex analysis by Walter Rudin which is a masterpiece in pure mathematics.