Calculus Examples

$\int_{0}^{2} 3 r^{3} d x$

Step 1

Apply the constant rule.

$3 r^{3} x]_{0}^{2}$

Step 2

Substitute and simplify.

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Step 2.1

Evaluate $3 r^{3} x$ at $2$ and at $0$ .

$(3 r^{3} \cdot 2) - 3 r^{3} \cdot 0$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $2$ by $3$ .

$6 r^{3} - 3 r^{3} \cdot 0$

Step 2.2.2

Multiply $0$ by $- 3$ .

$6 r^{3} + 0 r^{3}$

Step 2.2.3

Multiply $0$ by $r^{3}$ .

$6 r^{3} + 0$

Step 2.2.4

Add $6 r^{3}$ and $0$ .

$6 r^{3}$

$6 r^{3}$

$6 r^{3}$

Step 3

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