Calculus Examples

$\sum_{i = 1}^{3} i^{4} - i^{3}$

Step 1

Expand the series for each value of $i$ .

$1^{4} - 1^{3} + 2^{4} - 2^{3} + 3^{4} - 3^{3}$

Step 2

Simplify.

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Step 2.1

Raise $1$ to the power of $4$ .

$1 - 1^{3} + 2^{4} - 2^{3} + 3^{4} - 3^{3}$

Step 2.2

Raise $1$ to the power of $3$ .

$1 - 1 \cdot 1 + 2^{4} - 2^{3} + 3^{4} - 3^{3}$

Step 2.3

Multiply $- 1$ by $1$ .

$1 - 1 + 2^{4} - 2^{3} + 3^{4} - 3^{3}$

Step 2.4

Subtract $1$ from $1$ .

$0 + 2^{4} - 2^{3} + 3^{4} - 3^{3}$

Step 2.5

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

$0 + 16 - 2^{3} + 3^{4} - 3^{3}$

Step 2.6

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

$0 + 16 - 1 \cdot 8 + 3^{4} - 3^{3}$

Step 2.7

Multiply $- 1$ by $8$ .

$0 + 16 - 8 + 3^{4} - 3^{3}$

Step 2.8

Subtract $8$ from $16$ .

$0 + 8 + 3^{4} - 3^{3}$

Step 2.9

Add $0$ and $8$ .

$8 + 3^{4} - 3^{3}$

Step 2.10

Raise $3$ to the power of $4$ .

$8 + 81 - 3^{3}$

Step 2.11

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

$8 + 81 - 1 \cdot 27$

Step 2.12

Multiply $- 1$ by $27$ .

$8 + 81 - 27$

Step 2.13

Subtract $27$ from $81$ .

$8 + 54$

Step 2.14

Add $8$ and $54$ .

$62$

$62$

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