Question

Hello, I'd appreciate any help with the following question below:

Information:
g(x)= 4 (x+1)^(-2/3)

f(x)= ∫ g(t) dt

The Question:
What is f(26) ?


(NOTE: I don't know how to do this on a key board, so I'll just say that while I did type an Indefinite integral for "f(x)" it is actually a Definite integral with the bounds being from 0 to "x" meaning the 0 is on the bottom of the integral sign and the x is on the top of the integral sign).

Answer 1

so you want
f(x)= ∫ 4 (x+1)^(-2/3) dx from 0 to x
= (4/(1/3) (x+1)^(1/3) from 0 to x

= 12(x+1)^1/3

so f(26) = 12(27)^(1/3)
= 12(3) = 36

Answer 2

I jumped to conclusion when I subbed in the 0

(4/(1/3) (x+1)^(1/3) from 0 to x
= 12(x+1)^1/3 from 0 to x

should have given me:
12 (x+1)^(1/3) - 12(1)^(1/3)
= 12 (x+1)^(1/3) - 12

f(x) = 12 (x+1)^(1/3) - 12
f(26) = 12(3) - 12
= 24

Answer 3

AH! I understand, thank you Reiny!