Question

determine the indefinite integral at the point (2,6) if the formula for the slope is given as : -2x to the power of 3 -4x +2

Answer 1

Do you mean,\[\int\limits_{}{}-2x^3-4x+2dx\]?

Answer 2

If so, all you do is integrate to obtain the family of solutions,\[y=-\frac{2x^4}{4}-\frac{4x^2}{2}+2x+c\]that is\[y=-\frac{x^4}{2}-2x^2+2x+c\]At the point (2,6), you'd have\[6=-\frac{2^4}{2}-2(2)^2+2(2)+c\]

Answer 3

Solve for c:

c = 18

Answer 4

\[-\frac{x^4}{2}-2x^2+2x+18\]is your integral.