Calculus Examples

$\sum_{i = 3}^{5} i^{2} - 10$

Step 1

Expand the series for each value of $i$ .

$3^{2} - 10 + 4^{2} - 10 + 5^{2} - 10$

Step 2

Simplify.

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Step 2.1

Raise $3$ to the power of $2$ .

$9 - 10 + 4^{2} - 10 + 5^{2} - 10$

Step 2.2

Subtract $10$ from $9$ .

$- 1 + 4^{2} - 10 + 5^{2} - 10$

Step 2.3

Raise $4$ to the power of $2$ .

$- 1 + 16 - 10 + 5^{2} - 10$

Step 2.4

Subtract $10$ from $16$ .

$- 1 + 6 + 5^{2} - 10$

Step 2.5

Add $- 1$ and $6$ .

$5 + 5^{2} - 10$

Step 2.6

Raise $5$ to the power of $2$ .

$5 + 25 - 10$

Step 2.7

Subtract $10$ from $25$ .

$5 + 15$

Step 2.8

Add $5$ and $15$ .

$20$

$20$

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