Posted by
**drwls** on
.

The indefinite integral, or which call the "antiderivative", of f'(x)=6x-8x^3

is f(x) = 3x^2 - 2x^4 + C

where C is any constant.

Plug in x = 2 to that to see what C is.

3 = 3*4 - 2*16 + C

Determine the antiderivative of the following function given the initial condition: f'(x)=6x-8x^3 given that

f(2)=3

f'(x)=6x-8x^3

f(x)= 6x^2/2 - 8x^4/4 + C

Put in x=2 and solve for C