Calculus Examples

$\int_{0}^{6} f (x) d x$

Step 1

Apply the constant rule.

$f (x) x]_{0}^{6}$

Step 2

Substitute and simplify.

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Step 2.1

Evaluate $f (x) x$ at $6$ and at $0$ .

$(f (x) \cdot 6) - f (x) \cdot 0$

Step 2.2

Simplify.

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Step 2.2.1

Move $6$ to the left of $f (x)$ .

$6 \cdot f (x) - f (x) \cdot 0$

Step 2.2.2

Multiply $0$ by $- 1$ .

$6 f (x) + 0 f (x)$

Step 2.2.3

Multiply $0$ by $f (x)$ .

$6 f (x) + 0$

Step 2.2.4

Add $6 f (x)$ and $0$ .

$6 f (x)$

$6 f (x)$

$6 f (x)$

Step 3

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