Approximation of an integral when function varies little

44 Views Asked by At

I am doing a circuit analysis and getting this approximation below. I don't know if it is correct or not. I can check it for several cases but I think there is a formal proof of this.

Can anyone prove or show me how to prove this or even reject this?

$$\int_{a}^{b} f(x) dx ≈ f(x)*(b-a) $$ where f(x) varies little over the range [a, b].

Update:

After reading AntonioVargas comment, I reviewed the integral and actually the upper and lower limit are functions of x.

I will provide more context. I am studying the lecture here and at page 18, I think there is an approximation. Note that Vg(t) (the dotted line) is not a constant but a function of t.

enter image description here