Properties of integrals (1 Viewer)

[zeek]

Hey guys... i've got a question that i need to integrate using one of the properties of integrals, mainly using...

int(Lim a to 0) [f(x) dx] = int(Lim a to 0) [f(a-x) dx]

The question is:

int(Lim 1 to 0) [10100x(1-x)⁹⁹ dx]

thx

 

[STx]

for the limits you meant: 0-->1 right?

∫₀ ¹ 10100x(1-x)⁹⁹dx
= ∫₀ ¹ (1-10100x).[1-(1-10100x)]⁹⁹dx
= ∫₀ ¹ (1-10100x).(10100x)⁹⁹dx
= ∫₀ ¹ (10100x⁹⁹-10100x¹⁰⁰)dx
= [10100x¹⁰⁰/100 - 10100x¹⁰¹/101]₀ ¹
= (101-100)-(0-0)
= 1 #

 

[zeek]

yep lol i jst saw it now... thx