Calculus Examples

$\int_{0}^{1} \sqrt{144 - {(1.5)}^{2}} d x$

Step 1

Simplify.

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Step 1.1

Raise $1.5$ to the power of $2$ .

$\int_{0}^{1} \sqrt{144 - 1 \cdot 2.25} d x$

Step 1.2

Multiply $- 1$ by $2.25$ .

$\int_{0}^{1} \sqrt{144 - 2.25} d x$

Step 1.3

Subtract $2.25$ from $144$ .

$\int_{0}^{1} \sqrt{141.75} d x$

$\int_{0}^{1} \sqrt{141.75} d x$

Step 2

Apply the constant rule.

$\sqrt{141.75} x]_{0}^{1}$

Step 3

Substitute and simplify.

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Step 3.1

Evaluate $\sqrt{141.75} x$ at $1$ and at $0$ .

$(\sqrt{141.75} \cdot 1) - \sqrt{141.75} \cdot 0$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $\sqrt{141.75}$ by $1$ .

$\sqrt{141.75} - \sqrt{141.75} \cdot 0$

Step 3.2.2

Multiply $0$ by $- 1$ .

$\sqrt{141.75} + 0 \sqrt{141.75}$

Step 3.2.3

Multiply $0$ by $\sqrt{141.75}$ .

$\sqrt{141.75} + 0$

Step 3.2.4

Add $\sqrt{141.75}$ and $0$ .

$\sqrt{141.75}$

$\sqrt{141.75}$

$\sqrt{141.75}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{141.75}$

Decimal Form:

$11.90588089 \dots$

Step 5

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