Calculus Examples

$\int_{0}^{0.3} 2 e^{- x^{2}} d x$

Step 1

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

$2 \int_{0}^{0.3} e^{- x^{2}} d x$

Step 2

$\int_{0}^{0.3} e^{- x^{2}} d x$ is a special integral. The integral is the error function.

$2 (erf (x)]_{0}^{0.3})$

Step 3

Substitute and simplify.

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Step 3.1

Evaluate $erf (x)$ at $0.3$ and at $0$ .

$2 ((erf (x)) - erf (x))$

Step 3.2

Simplify.

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Step 3.2.1

Subtract $erf (x)$ from $erf (x)$ .

$2 \cdot 0$

Step 3.2.2

Multiply $2$ by $0$ .

$0$

Step 4