Find the Function g(r)=25-3r

$g (r) = 25 - 3 r$

Step 1

The function $G (r)$ can be found by evaluating the indefinite integral of the derivative $g (r)$ .

$G (r) = \int g (r) d r$

Step 2

Split the single integral into multiple integrals.

$\int 25 d r + \int - 3 r d r$

Step 3

Apply the constant rule.

$25 r + C + \int - 3 r d r$

Step 4

Since $- 3$ is constant with respect to $r$ , move $- 3$ out of the integral.

$25 r + C - 3 \int r d r$

Step 5

By the Power Rule, the integral of $r$ with respect to $r$ is $\frac{1}{2} r^{2}$ .

$25 r + C - 3 (\frac{1}{2} r^{2} + C)$

Step 6

Simplify.

$25 r - 3 (\frac{1}{2}) r^{2} + C$

Simplify.

Combine $- 3$ and $\frac{1}{2}$ .

$25 r + \frac{- 3}{2} r^{2} + C$

Move the negative in front of the fraction.

$25 r - \frac{3}{2} r^{2} + C$

Step 7

The function $G$ if derived from the integral of the derivative of the function. This is valid by the fundamental theorem of calculus.

$G (r) = 25 r - \frac{3}{2} r^{2} + C$