Studying the monotony of an integral I'm trying to understand the following exercise:
Be $f: \mathbb{R} \rightarrow \mathbb{R}$ a continuous function, such that $f(x) \ge 0,\forall x \ge0$
Study the monotonicity of the following function: $g(x) := \int_{0}^{x^2} f(t)dt$
I'm still new to integrals and I'm lost on how should I start solving this.
Any tips are welcome!
Thanks

By the FTC, if $\;F(x)\;$ is a primitive of $\;f\;$ (it exists since $\;f\;$ is continuous), then
$$\int_0^{x^2}f(t)\,dt=F(x^2)-F(0)\implies\left(\int_0^{x^2}f(t)\,dt\right)'=\left(F(x^2)-F(0)\right)'\stackrel{\text{chain rule}}=2xF'(x^2)$$
Well, can you now say something about the sign of $\;g'(x)\;$ and thus about monotony of $\;g\;$ ?
