Final answer:
The integral ∫(14/8/4x²)dx from -2 is convergent.
Step-by-step explanation:
To determine whether the integral ∫(14/8/4x²)dx from -2 is convergent or divergent, we need to evaluate the integral and check for convergence. Let's start by simplifying the integral: ∫(14/8/4x²)dx = ∫(7/4x²)dx = (7/4) ∫(1/x²)dx.
Next, we evaluate the integral: ∫(1/x²)dx = -1/x.
Now we can find the value of the integral from x = -2: ∫(7/4x²)dx = (7/4) ∫(1/x²)dx = (7/4)(-1/(-2)) = 7/8.
Since the value of the integral is finite, the integral ∫(14/8/4x²)dx from -2 is convergent.