Calculus Examples

$\int_{0}^{1} \sqrt{144 - 3^{2}} d x$

Step 1

Simplify.

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Step 1.1

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

$\int_{0}^{1} \sqrt{144 - 1 \cdot 9} d x$

Step 1.2

Multiply $- 1$ by $9$ .

$\int_{0}^{1} \sqrt{144 - 9} d x$

Step 1.3

Subtract $9$ from $144$ .

$\int_{0}^{1} \sqrt{135} d x$

$\int_{0}^{1} \sqrt{135} d x$

Step 2

Apply the constant rule.

$\sqrt{135} x]_{0}^{1}$

Step 3

Simplify the answer.

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Step 3.1

Substitute and simplify.

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Step 3.1.1

Evaluate $\sqrt{135} x$ at $1$ and at $0$ .

$(\sqrt{135} \cdot 1) - \sqrt{135} \cdot 0$

Step 3.1.2

Simplify.

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Step 3.1.2.1

Multiply $\sqrt{135}$ by $1$ .

$\sqrt{135} - \sqrt{135} \cdot 0$

Step 3.1.2.2

Multiply $0$ by $- 1$ .

$\sqrt{135} + 0 \sqrt{135}$

Step 3.1.2.3

Multiply $0$ by $\sqrt{135}$ .

$\sqrt{135} + 0$

Step 3.1.2.4

Add $\sqrt{135}$ and $0$ .

$\sqrt{135}$

$\sqrt{135}$

$\sqrt{135}$

Step 3.2

Simplify.

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Step 3.2.1

Rewrite $135$ as $3^{2} \cdot 15$ .

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Step 3.2.1.1

Factor $9$ out of $135$ .

$\sqrt{9 (15)}$

Step 3.2.1.2

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 15}$

$\sqrt{3^{2} \cdot 15}$

Step 3.2.2

Pull terms out from under the radical.

$3 \sqrt{15}$

$3 \sqrt{15}$

$3 \sqrt{15}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{15}$

Decimal Form:

$11.61895003 \dots$

Step 5

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