Question

How do you use the reverse power rule?

f(x)=5x^4-4x^3+3x^2-2x+1

Answer 1

add one to the exponent and divide by that number
\[\int x^ndx=\frac{x^{n+1}}{n+1}\]

Answer 2

how do i apply that to this problem?

Answer 3

piece by piece

Answer 4

can you give an example? *right now i'm just studying, so use can use the problem above i made up*

Answer 5

\[\int 5x^4dx=5\times\frac{x^{4+1}}{4+1}\]

Answer 6

i.e.
\[5\frac{x^5}{5}=x^5\]

Answer 7

\[f(x)=ax^2+bx+c \\ F(x)=a \frac{x^{2+1}}{2+1}+b \frac{x^{1+1}}{1+1}+cx+d\]
Where F'=f

Answer 8

that was another example

Answer 9

could you do 5x^4 step-by-step?

Answer 10

i don't get this :(

Answer 11

\[\text{ if } g(x)=5x^4 \text{ then } G(x)=5 \cdot \frac{x^{4+1}}{4+1}+c\]

Answer 12

That is the absolute first step

Answer 13

\[f(x)=ax^{n} \text{ then } F(x)=a \cdot \frac{x^{n+1}}{n+1} +c \text{ where } n \neq -1 \]