Calculus Examples

$R' (x) = 600 - 0.6 x$

Step 1

The function $R (x)$ can be found by evaluating the indefinite integral of the derivative $R' (x)$ .

$R (x) = \int R' (x) d x$

Step 2

Split the single integral into multiple integrals.

$\int 600 d x + \int - 0.6 x d x$

Step 3

Apply the constant rule.

$600 x + C + \int - 0.6 x d x$

Step 4

Since $- 0.6$ is constant with respect to $x$ , move $- 0.6$ out of the integral.

$600 x + C - 0.6 \int x d x$

Step 5

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

$600 x + C - 0.6 (\frac{1}{2} x^{2} + C)$

Step 6

Simplify.

Tap for more steps...

Step 6.1

Simplify.

$600 x - 0.6 (\frac{1}{2}) x^{2} + C$

Step 6.2

Simplify.

Tap for more steps...

Step 6.2.1

Combine $- 0.6$ and $\frac{1}{2}$ .

$600 x + \frac{- 0.6}{2} x^{2} + C$

Step 6.2.2

Move the negative in front of the fraction.

$600 x - \frac{0.6}{2} x^{2} + C$

Step 6.3

Simplify.

Tap for more steps...

Step 6.3.1

Divide $0.6$ by $2$ .

$600 x - 1 \cdot 0.3 x^{2} + C$

Step 6.3.2

Multiply $- 1$ by $0.3$ .

$600 x - 0.3 x^{2} + C$

Step 7

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

$R (x) = 600 x - 0.3 x^{2} + C$