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(A) The anti-derivative of $e^{2x}$ is a function $F(x)$ such that $F'(x) = e^{2x}$.We know that the derivative of $e^{2x}$ with respect to $x$ is:$\f

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The anti-derivative of $e^{2x}$ is a function $F(x)$ such that $F'(x) = e^{2x}$.We know that the derivative of $e^{2x}$ with respect to $x$ is:$\frac{d}{dx}(e^{2x}) = 2e^{2x}$To isolate $e^{2x}$,we divide both sides by $2$:$e^{2x} = \frac{1}{2} \frac{d}{dx}(e^{2x})$Using the linearity property of the derivative,we can write:$e^{2x} = \frac{d}{dx}\left(\frac{1}{2} e^{2x}\right)$Thus,by the method of inspection,the anti-derivative of $e^{2x}$ is $\frac{1}{2} e^{2x}$.

Find an anti-derivative (or integral) of the function $e^{2x}$ by the method of inspection.

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