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Maths-

General

Easy

Question

$not stretchy integral e to the power of x to the power of 2 end exponent end exponent x d x$ is equal to

$e^{x^{2}}$
$\frac{1}{2} e^{x^{2}}$
$2 e^{x^{2}}$
$\frac{e^{x^{2}} - x^{2}}{2}$

The correct answer is: $fraction numerator 1 over denominator 2 end fraction e to the power of x to the power of 2 end exponent end exponent$

$not stretchy integral e to the power of x to the power of 2 end exponent end exponent. x d x equals fraction numerator 1 over denominator 2 end fraction not stretchy integral left parenthesis 2 x right parenthesis e to the power of x to the power of 2 end exponent end exponent d x$
$equals fraction numerator 1 over denominator 2 end fraction not stretchy integral e to the power of t end exponent d t equals fraction numerator 1 over denominator 2 end fraction e to the power of t end exponent equals fraction numerator 1 over denominator 2 end fraction e to the power of x to the power of 2 end exponent end exponent$ , (Put $x to the power of 2 end exponent equals t rightwards double arrow d t equals 2 x d x right parenthesis$ .

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