Calculus Examples

$\int_{a}^{b} x^{2} d x$

Step 1

By the Power Rule, the integral of $x^{2}$ with respect to $x$ is $\frac{1}{3} x^{3}$ .

$\frac{1}{3} x^{3}]_{a}^{b}$

Step 2

Evaluate $\frac{1}{3} x^{3}$ at $b$ and at $a$ .

$\frac{1}{3} b^{3} - \frac{1}{3} a^{3}$

Step 3

Simplify each term.

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Step 3.1

Combine $\frac{1}{3}$ and $b^{3}$ .

$\frac{b^{3}}{3} - \frac{1}{3} a^{3}$

Step 3.2

Combine $a^{3}$ and $\frac{1}{3}$ .

$\frac{b^{3}}{3} - \frac{a^{3}}{3}$