Question

Integrate the following with respect to x.

If f'(x) = e^x and f(0) = 2, then find f(x)

Answer 1

f'(x) = e^x

Integrating both sides of the equation

`int "f'"(x)  "d"x  int "e"^x  "d"x`

⇒ f(x) = e^x + c

Given f(0) = 2

2 = e⁰ + c

⇒ c = 1

Thus f(x) = e^x + 1