Calculus Examples

$30 (25 - t^{2})$

Step 1

Multiply $30 (25 - t^{2})$ .

$\int 30 \cdot 25 + 30 (- t^{2}) d t$

Step 2

Simplify.

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Step 2.1

Multiply $30$ by $25$ .

$\int 750 + 30 (- t^{2}) d t$

Step 2.2

Multiply $- 1$ by $30$ .

$\int 750 - 30 t^{2} d t$

Step 3

Split the single integral into multiple integrals.

$\int 750 d t + \int - 30 t^{2} d t$

Step 4

Apply the constant rule.

$750 t + C + \int - 30 t^{2} d t$

Step 5

Since $- 30$ is constant with respect to $t$ , move $- 30$ out of the integral.

$750 t + C - 30 \int t^{2} d t$

Step 6

By the Power Rule, the integral of $t^{2}$ with respect to $t$ is $\frac{1}{3} t^{3}$ .

$750 t + C - 30 (\frac{1}{3} t^{3} + C)$

Step 7

Simplify.

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Step 7.1

Simplify.

$750 t - 30 (\frac{1}{3}) t^{3} + C$

Step 7.2

Simplify.

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Step 7.2.1

Combine $- 30$ and $\frac{1}{3}$ .

$750 t + \frac{- 30}{3} t^{3} + C$

Step 7.2.2

Cancel the common factor of $- 30$ and $3$ .

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Step 7.2.2.1

Factor $3$ out of $- 30$ .

$750 t + \frac{3 \cdot - 10}{3} t^{3} + C$

Step 7.2.2.2

Cancel the common factors.

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Step 7.2.2.2.1

Factor $3$ out of $3$ .

$750 t + \frac{3 \cdot - 10}{3 (1)} t^{3} + C$

Step 7.2.2.2.2

Cancel the common factor.

$750 t + \frac{3 \cdot - 10}{3 \cdot 1} t^{3} + C$

Step 7.2.2.2.3

Rewrite the expression.

$750 t + \frac{- 10}{1} t^{3} + C$

Step 7.2.2.2.4

Divide $- 10$ by $1$ .

$750 t - 10 t^{3} + C$