Calculus Examples

$\int_{0}^{3} \sqrt{5} d x$

Step 1

Apply the constant rule.

$\sqrt{5} x]_{0}^{3}$

Step 2

Substitute and simplify.

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Step 2.1

Evaluate $\sqrt{5} x$ at $3$ and at $0$ .

$(\sqrt{5} \cdot 3) - \sqrt{5} \cdot 0$

Step 2.2

Simplify.

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Step 2.2.1

Move $3$ to the left of $\sqrt{5}$ .

$3 \cdot \sqrt{5} - \sqrt{5} \cdot 0$

Step 2.2.2

Multiply $0$ by $- 1$ .

$3 \sqrt{5} + 0 \sqrt{5}$

Step 2.2.3

Multiply $0$ by $\sqrt{5}$ .

$3 \sqrt{5} + 0$

Step 2.2.4

Add $3 \sqrt{5}$ and $0$ .

$3 \sqrt{5}$

$3 \sqrt{5}$

$3 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{5}$

Decimal Form:

$6.70820393 \dots$

Step 4

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