Calculus Examples

$\frac{d A}{d t} = 2 π (40) (0.04)$

Step 1

Rewrite the equation.

$d A = 2 π (40) (0.04) d t$

Step 2

Integrate both sides.

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Step 2.1

Set up an integral on each side.

$\int d A = \int 2 π \cdot 40 \cdot 0.04 d t$

Step 2.2

Apply the constant rule.

$A + C_{1} = \int 2 π \cdot 40 \cdot 0.04 d t$

Step 2.3

Integrate the right side.

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Step 2.3.1

Simplify.

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Step 2.3.1.1

Multiply $40$ by $2$ .

$A + C_{1} = \int 80 π \cdot 0.04 d t$

Step 2.3.1.2

Multiply $0.04$ by $80$ .

$A + C_{1} = \int 3.2 π d t$

Step 2.3.1.3

Multiply $3.2$ by $π$ .

$A + C_{1} = \int 10.05309649 d t$

$A + C_{1} = \int 10.05309649 d t$

Step 2.3.2

Apply the constant rule.

$A + C_{1} = 10.05309649 t + C_{2}$

$A + C_{1} = 10.05309649 t + C_{2}$

Step 2.4

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

$A = 10.05309649 t + K$

$A = 10.05309649 t + K$

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