# What should be used?

Calculus Level 4

Let $$f\colon\mathbb R \to \mathbb R$$ be a continuous function satisfying $$\displaystyle f(x) + \int_0^x t f(t) \, dt + x^2 = 0$$ for all real $$x$$.

Which of the following is true?

Source: KVPY 2015 (SX/SB stream).

×