Calculus Examples

$\int_{0}^{4} x^{3} d x$

Step 1

By the Power Rule, the integral of $x^{3}$ with respect to $x$ is $\frac{1}{4} x^{4}$ .

$\frac{1}{4} x^{4}]_{0}^{4}$

Step 2

Substitute and simplify.

Tap for more steps...

Step 2.1

Evaluate $\frac{1}{4} x^{4}$ at $4$ and at $0$ .

$(\frac{1}{4} \cdot 4^{4}) - \frac{1}{4} \cdot 0^{4}$

Step 2.2

Simplify.

Tap for more steps...

Step 2.2.1

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

$\frac{1}{4} \cdot 256 - \frac{1}{4} \cdot 0^{4}$

Step 2.2.2

Combine $\frac{1}{4}$ and $256$ .

$\frac{256}{4} - \frac{1}{4} \cdot 0^{4}$

Step 2.2.3

Cancel the common factor of $256$ and $4$ .

Tap for more steps...

Step 2.2.3.1

Factor $4$ out of $256$ .

$\frac{4 \cdot 64}{4} - \frac{1}{4} \cdot 0^{4}$

Step 2.2.3.2

Cancel the common factors.

Tap for more steps...

Step 2.2.3.2.1

Factor $4$ out of $4$ .

$\frac{4 \cdot 64}{4 (1)} - \frac{1}{4} \cdot 0^{4}$

Step 2.2.3.2.2

Cancel the common factor.

$\frac{4 \cdot 64}{4 \cdot 1} - \frac{1}{4} \cdot 0^{4}$

Step 2.2.3.2.3

Rewrite the expression.

$\frac{64}{1} - \frac{1}{4} \cdot 0^{4}$

Step 2.2.3.2.4

Divide $64$ by $1$ .

$64 - \frac{1}{4} \cdot 0^{4}$

Step 2.2.4

Raising $0$ to any positive power yields $0$ .

$64 - \frac{1}{4} \cdot 0$

Step 2.2.5

Multiply $0$ by $- 1$ .

$64 + 0 (\frac{1}{4})$

Step 2.2.6

Multiply $0$ by $\frac{1}{4}$ .

$64 + 0$

Step 2.2.7

Add $64$ and $0$ .

$64$

Step 3