First slide

Introduction to integration

Question

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

Easy

A

$e^{100}$
B

100
C

2
D

none of these

Solution

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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