Let f(x) = and g '(x) = f(x). Find g(x) if g(0) = 4.

Question

 

Let f(x) =  and g '(x) = f(x). Find g(x) if g(0) = 4.

Answer 1

g(x) is the antiderivative of f(x)

Integrating, g(x) = ∑a_nxⁿ⁺¹/(n+1) + C a_n is a list of constants, so not affected by the integration

g(0) = 0+C = 4, so C= 4

_∞

The answer is 4 + ∑a_nxⁿ⁺¹/(n+1)

n=0