Calculus Examples

$\int_{0}^{2} \sqrt{4 - {0.75}^{2}} d x$

Step 1

Simplify.

Tap for more steps...

Step 1.1

Raise $0.75$ to the power of $2$ .

$\int_{0}^{2} \sqrt{4 - 1 \cdot 0.5625} d x$

Step 1.2

Multiply $- 1$ by $0.5625$ .

$\int_{0}^{2} \sqrt{4 - 0.5625} d x$

Step 1.3

Subtract $0.5625$ from $4$ .

$\int_{0}^{2} \sqrt{3.4375} d x$

$\int_{0}^{2} \sqrt{3.4375} d x$

Step 2

Apply the constant rule.

$\sqrt{3.4375} x]_{0}^{2}$

Step 3

Substitute and simplify.

Tap for more steps...

Step 3.1

Evaluate $\sqrt{3.4375} x$ at $2$ and at $0$ .

$(\sqrt{3.4375} \cdot 2) - \sqrt{3.4375} \cdot 0$

Step 3.2

Simplify.

Tap for more steps...

Step 3.2.1

Move $2$ to the left of $\sqrt{3.4375}$ .

$2 \cdot \sqrt{3.4375} - \sqrt{3.4375} \cdot 0$

Step 3.2.2

Multiply $0$ by $- 1$ .

$2 \sqrt{3.4375} + 0 \sqrt{3.4375}$

Step 3.2.3

Multiply $0$ by $\sqrt{3.4375}$ .

$2 \sqrt{3.4375} + 0$

Step 3.2.4

Add $2 \sqrt{3.4375}$ and $0$ .

$2 \sqrt{3.4375}$

$2 \sqrt{3.4375}$

$2 \sqrt{3.4375}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{3.4375}$

Decimal Form:

$3.70809924 \dots$

Step 5

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