Question

Determine if the improper integral converges or diverges. if it converges, what does it converge to?

∫₀⁵d x/√(5-x)

Answer 1

The given improper integral converges to 2√5.

Step-by-step explanation:

To determine if the given improper integral converges or diverges, we need to evaluate it.

The given integral is ∫₀⁵ dx/√(5-x).

We can evaluate this integral by making the substitution u = 5 - x. Differentiating with respect to x, we get du = -dx.

Now, substituting the values, the integral becomes -∫₅⁰ du/√u.

Integrating, we get -2√u from 5 to 0, which simplifies to 2√5.

Since the integral evaluates to a finite value, it converges to 2√5.