Calculus Examples

$\int_{0}^{8} \sqrt{64 - 3^{2}} d x$

Step 1

Simplify.

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Step 1.1

Raise $3$ to the power of $2$ .

$\int_{0}^{8} \sqrt{64 - 1 \cdot 9} d x$

Step 1.2

Multiply $- 1$ by $9$ .

$\int_{0}^{8} \sqrt{64 - 9} d x$

Step 1.3

Subtract $9$ from $64$ .

$\int_{0}^{8} \sqrt{55} d x$

$\int_{0}^{8} \sqrt{55} d x$

Step 2

Apply the constant rule.

$\sqrt{55} x]_{0}^{8}$

Step 3

Substitute and simplify.

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Step 3.1

Evaluate $\sqrt{55} x$ at $8$ and at $0$ .

$(\sqrt{55} \cdot 8) - \sqrt{55} \cdot 0$

Step 3.2

Simplify.

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Step 3.2.1

Move $8$ to the left of $\sqrt{55}$ .

$8 \cdot \sqrt{55} - \sqrt{55} \cdot 0$

Step 3.2.2

Multiply $0$ by $- 1$ .

$8 \sqrt{55} + 0 \sqrt{55}$

Step 3.2.3

Multiply $0$ by $\sqrt{55}$ .

$8 \sqrt{55} + 0$

Step 3.2.4

Add $8 \sqrt{55}$ and $0$ .

$8 \sqrt{55}$

$8 \sqrt{55}$

$8 \sqrt{55}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt{55}$

Decimal Form:

$59.32958789 \dots$

Step 5

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