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Question
Integrate the following with respect to x.
If f'(x) = ex and f(0) = 2, then find f(x)
Solution
f'(x) = ex
Integrating both sides of the equation
`int "f'"(x) "d"x int "e"^x "d"x`
⇒ f(x) = ex + c
Given f(0) = 2
2 = e0 + c
⇒ c = 1
Thus f(x) = ex + 1
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