Question

what is the most general antiderivative of the function F(x)= ½ + ¾ x^2 -4/5 x^3

Answer 1

Ok so we need to find the anti-derivative of this?\[\Large F(x) \quad=\quad \frac{1}{2}+\frac{3}{4}x^2-\frac{4}{5}x^3\]

Answer 2

Are you familiar with the process for applying the `Power Rule` in reverse?
Because that's what we'll be doing here.

Answer 3

When we take the derivatives, we:
~Bring the exponent down as a coefficient being multiplied.
~Subtract 1 from the exponent.


When we need to find an anti-derivative, we do the opposite and in the reverse order:
~Add 1 to the exponent.
~Bring the new exponent down as a coefficient being divided.

Answer 4

Example:
\[\Large F(x)=x^3\]
f(x) represents the antiderivative of F(x):\[\Large f(x)=\frac{1}{3+1}x^{3+1}\quad=\quad \frac{1}{4}x^4\]