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If it is known that at the point $x = 1$ two antiderivatives of $f (x) = e^{x}$ differ by $2$ The difference of these antiderivatives at $x = 100$ is

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e^{100}

100

none of these

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detailed solution

Correct option is C

Let the two antiderivates be $e^{x} + C_{1}$ and $e^{x} + C_{2}$

At $x = 1, C_{1} - C_{2} = 2$

At $x = 100$ it is $e^{100} + C_{1} - e^{100} - C_{2}$

$= C_{1} - C_{2} = 2$

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If it is known that at the point x = 1 two antiderivatives of f(x)=ex differ by 2 The difference of these antiderivatives at x =100 is

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If it is known that at the point $x = 1$ two antiderivatives of $f (x) = e^{x}$ differ by $2$ The difference of these antiderivatives at $x = 100$ is