1. Funtions and Primitives

Hey there!
I was given the following exercise:

The function $\displaystyle h:\mathbb{R} \longrightarrow \mathbb{R}$ is consistent with the following:
$\displaystyle h'(x)=(3x-2)\sqrt{1+|2x|}$

and

$\displaystyle h(1)=0$.

Calculate $\displaystyle h(-1)$.

So I have tried to calculate the primitive of the function h'(x) so I could get to h(x) but everything I've tried calculating doesn't give me h(1)=0. Even inputing h'(x) into Wolfram Integrator gives me a certain h(x) that doesn't comply with h(1)=0.

Could you please have a look at it and let me know how you'd do it?

2. Originally Posted by mei
Hey there!
I was given the following exercise:

The function $\displaystyle h:\mathbb{R} \longrightarrow \mathbb{R}$ is consistent with the following:
$\displaystyle h'(x)=(3x-2)\sqrt{1+|2x|}$

and

$\displaystyle h(1)=0$.

Calculate $\displaystyle h(-1)$.

So I have tried to calculate the primitive of the function h'(x) so I could get to h(x) but everything I've tried calculating doesn't give me h(1)=0. Even inputing h'(x) into Wolfram Integrator gives me a certain h(x) that doesn't comply with h(1)=0.

Could you please have a look at it and let me know how you'd do it?