Calculus Examples

$\frac{1}{2} \cdot e^{2} - \frac{1}{2}$

Step 1

Simplify terms.

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Step 1.1

Combine $\frac{1}{2}$ and $e^{2}$ .

$\frac{e^{2}}{2} - \frac{1}{2}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{e^{2} - 1}{2}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

$\frac{e^{2} - 1^{2}}{2}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = e$ and $b = 1$ .

$\frac{(e + 1) (e - 1)}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{(e + 1) (e - 1)}{2}$

Decimal Form:

$3.19452804 \dots$