looks fine to me ...
I have f(x)= and I want to find F(x)
I am also given that F(1)=0
I get F(x)=
and since F(1)=0
F(x)=
F(x)=
F(x)=
so c=17/6
however the above is wrong somewhere. I just don't see where
Hi-
I Thought some might benefit from seeing all the steps to this problem:
Given:
f ' (x) = 8 / x^3 - 7 / x^7 Where f(1)=0
Rewrite:
f ' (x) = 8*x^(-3) - 7*x^(-7)
Integrate:
8*x^(-3+1) 7*x^(-7+1)
= ∫ -------------- - ---------------
(-3+1) (-7+1)
= 8*x^(-2)/(-2) - 7*x^(-6)/(-6)
= -4*x^(-2) + (7/6)*x^(-6) + C
Answer:
f (x) = -4 / x^2 + 7 / 6*x^6 + C
At f (1) = 0
f (1) = -4 / (1)^2 + 7 / 6*(1)^6 + C = 0
= -4 + 7/6 + C = 0
Common Denominator:
= -24 / 6 + 7 / 6 + C = 0
= -17 / 6 + C = 0
C = 17 / 6
Answer:
f (x) = -4 / x^2 + 7 / 6*x^6 + 17 / 6