Question

Anti derivative question:

Answer 1

I suppose you want to find the antiderivative with respect to x
\[I=-\frac{ 1 }{ 12x^4 }\]
you can always check it by deriving
of course, this is the indefinite integral

Answer 2

let me rephrase the question:
\[f(x)=\frac{ 1 }{ 3x^3 }\]
State is the following is true:
1. \[\int\limits_{0}^{1} f(x) dx=0.5\]
2. the function \[F(x)=3-[\frac{ 1 }{ 6x^2 }]\]

Answer 3

if G(x) is the anti derivative of f(x) then G'(1)=\[2\frac{ 5}{ 6 }\]
in the range (0,infinity)

Answer 4

3*

Answer 5

if you want the definite integral:
\[\lim_{b \rightarrow \infty}(-\frac{ 1 }{ 12b^4 }+\frac{ 1 }{ 12})=\frac{ 1 }{ 12 }\]
P.S: The definite integral should have been:
\[-\frac{ 1 }{ 12x^4 }+C\]

Answer 6

@smarty20two how did you get to -1/12b^4 ?
Can you break it up for me in stages? thanks.

Answer 7

-1/12x^4 could be written as -(1/12)(x^-4)
you can keep the constant (-1/12) out and integrate x^-4
you get (-1/12)((x^(-4+1))/(-4+1))+C