Calculus Examples

$\int_{0}^{2} 9 {(1.5)}^{2} d x$

Step 1

Simplify.

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Step 1.1

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

$\int_{0}^{2} 9 \cdot 2.25 d x$

Step 1.2

Multiply $9$ by $2.25$ .

$\int_{0}^{2} 20.25 d x$

$\int_{0}^{2} 20.25 d x$

Step 2

Apply the constant rule.

$20.25 x]_{0}^{2}$

Step 3

Substitute and simplify.

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Step 3.1

Evaluate $20.25 x$ at $2$ and at $0$ .

$(20.25 \cdot 2) - 20.25 \cdot 0$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $20.25$ by $2$ .

$40.5 - 20.25 \cdot 0$

Step 3.2.2

Multiply $- 20.25$ by $0$ .

$40.5 + 0$

Step 3.2.3

Add $40.5$ and $0$ .

$40.5$

$40.5$

$40.5$

Step 4

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