Question

Encuentra la función f(x) apartir de f'(x)=2x²+1 y f(0)=1​

Answer 1

Answer:

The primitive of f' is given by f = ∫f'.

So we have

f(x) = ∫f'(x)dx = ∫(2x²+1)dx = (2/3)x^3 +x+C where C is a constant. Now, as f(0)=1, we get C = 1 and therefore we have that

f(x) = (2/3)x^3 +x + 1 and I'm done.