Question

Seja f(x) uma função derivavel. Sabendo que f (0) = 0 e f'(x) = x + sin(x), é correto afirmar que:

Answer 1

$\large\boxed{\begin{array}{l}\sf f'(x)=x+sen(x)\\\\\displaystyle\sf f(x)=\int f'(x)dx\\\displaystyle\sf f(x)=\int(x+sen(x))dx\\\sf f(x)=\dfrac{x^2}{2}-cos(x)+k\\\sf f(0)=0\\\sf 0=\dfrac{0^2}{2}-cos(0)+k\\\\\sf k-1=0\\\sf k=1\\\sf f(x)=\dfrac{x^2}{2}-cos(x)+1\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~a}}}}\end{array}}$