Question

Determine whether the integral is convergent or divergent: ∫e^(-sqrt(y)).

A. Convergent
B. Divergent
C. Absolute convergence
D. Conditional convergence

Answer 1

The integral ∫e^(-sqrt(y)) converges.

Step-by-step explanation:

The term "integral" can have different meanings depending on the context. In mathematics, the integral is a fundamental concept that represents the signed area under a curve in a graph.

To determine if the integral ∫e^(-sqrt(y)) converges or diverges, we need to evaluate the limit as y approaches infinity. Let's set up the integral:

∫e^(-sqrt(y)) dy

Now, let's consider the behavior of the integrand as y approaches infinity. Since the square root of y grows without bound as y approaches infinity, the exponent becomes increasingly negative. Therefore, the integral converges.