Calculus Examples

$\int_{- 1}^{2} 2^{x} d x$

Step 1

This integral could not be completed using u-substitution. Mathway will use another method.

Step 2

The integral of $2^{x}$ with respect to $x$ is $\frac{2^{x}}{\ln (2)}$ .

$\frac{2^{x}}{\ln (2)}]_{- 1}^{2}$

Step 3

Substitute and simplify.

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Step 3.1

Evaluate $\frac{2^{x}}{\ln (2)}$ at $2$ and at $- 1$ .

$(\frac{2^{2}}{\ln (2)}) - \frac{2^{- 1}}{\ln (2)}$

Step 3.2

Simplify.

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Step 3.2.1

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

$\frac{4}{\ln (2)} - \frac{2^{- 1}}{\ln (2)}$

Step 3.2.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4}{\ln (2)} - \frac{\frac{1}{2}}{\ln (2)}$

Step 3.2.3

Rewrite $\frac{\frac{1}{2}}{\ln (2)}$ as a product.

$\frac{4}{\ln (2)} - (\frac{1}{2} \cdot \frac{1}{\ln (2)})$

Step 3.2.4

Multiply $\frac{1}{2}$ by $\frac{1}{\ln (2)}$ .

$\frac{4}{\ln (2)} - \frac{1}{2 \ln (2)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{\ln (2)} - \frac{1}{2 \ln (2)}$

Decimal Form:

$5.04943264 \dots$

Step 5