Calculus Examples

$\int_{0}^{2} 3^{x} d x$

Step 1

The integral of $3^{x}$ with respect to $x$ is $\frac{3^{x}}{\ln (3)}$ .

$\frac{3^{x}}{\ln (3)}]_{0}^{2}$

Step 2

Substitute and simplify.

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Step 2.1

Evaluate $\frac{3^{x}}{\ln (3)}$ at $2$ and at $0$ .

$(\frac{3^{2}}{\ln (3)}) - \frac{3^{0}}{\ln (3)}$

Step 2.2

Simplify.

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Step 2.2.1

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

$\frac{9}{\ln (3)} - \frac{3^{0}}{\ln (3)}$

Step 2.2.2

Anything raised to $0$ is $1$ .

$\frac{9}{\ln (3)} - \frac{1}{\ln (3)}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{9 - 1}{\ln (3)}$

Step 2.2.4

Subtract $1$ from $9$ .

$\frac{8}{\ln (3)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{\ln (3)}$

Decimal Form:

$7.28191381 \dots$

Step 4