Calculus Examples

$44.4 \frac{d y}{d t} = 0$

Step 1

Rewrite the equation.

$44.4 d y = 0 d t$

Step 2

Integrate both sides.

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Step 2.1

Set up an integral on each side.

$\int 44.4 d y = \int 0 d t$

Step 2.2

Apply the constant rule.

$44.4 y + C_{1} = \int 0 d t$

Step 2.3

Integrate the right side.

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Step 2.3.1

The integral of $0$ with respect to $t$ is $0$ .

$44.4 y + C_{1} = 0 + C_{2}$

Step 2.3.2

Add $0$ and $C_{2}$ .

$44.4 y + C_{1} = C_{2}$

$44.4 y + C_{1} = C_{2}$

Step 2.4

Group the constant of integration on the right side as $D$ .

$44.4 y = D$

$44.4 y = D$

Step 3

Divide each term in $44.4 y = D$ by $44.4$ and simplify.

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Step 3.1

Divide each term in $44.4 y = D$ by $44.4$ .

$\frac{44.4 y}{44.4} = \frac{D}{44.4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $44.4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{44.4 y}{44.4} = \frac{D}{44.4}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{D}{44.4}$

$y = \frac{D}{44.4}$

$y = \frac{D}{44.4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply by $1$ .

$y = \frac{1 D}{44.4}$

Step 3.3.2

Factor $44.4$ out of $44.4$ .

$y = \frac{1 D}{44.4 (1)}$

Step 3.3.3

Separate fractions.

$y = \frac{1}{44.4} \cdot \frac{D}{1}$

Step 3.3.4

Divide $1$ by $44.4$ .

$y = 0.0\overline{225} \frac{D}{1}$

Step 3.3.5

Divide $D$ by $1$ .

$y = 0.0\overline{225} D$

$y = 0.0\overline{225} D$

$y = 0.0\overline{225} D$

Step 4

Simplify the constant of integration.

$y = D$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$