Calculus Examples

$\sum_{i = 1}^{5} i (i + 4)$

Step 1

Simplify the summation.

Tap for more steps...

Step 1.1

Apply the distributive property.

$i \cdot i + i \cdot 4$

Step 1.2

Multiply $i$ by $i$ .

$i^{2} + i \cdot 4$

Step 1.3

Move $4$ to the left of $i$ .

$i^{2} + 4 i$

Step 1.4

Rewrite the summation.

$\sum_{i = 1}^{5} i^{2} + 4 i$

$\sum_{i = 1}^{5} i^{2} + 4 i$

Step 2

The formula for the summation of a constant is:

$\sum_{k = 1}^{n} c = c n$

Step 3

Substitute the values into the formula.

$(i^{2} + 4 i) (5)$

Step 4

Simplify.

Tap for more steps...

Step 4.1

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

$(- 1 + 4 i) \cdot 5$

Step 4.2

Apply the distributive property.

$- 1 \cdot 5 + 4 i \cdot 5$

Step 4.3

Multiply.

Tap for more steps...

Step 4.3.1

Multiply $- 1$ by $5$ .

$- 5 + 4 i \cdot 5$

Step 4.3.2

Multiply $5$ by $4$ .

$- 5 + 20 i$

$- 5 + 20 i$

$- 5 + 20 i$

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