Final answer:
To assess whether the integral from 0 to infinity of e^(-sqrt(y)) dy converges or diverges, we examine the behavior of the integrand as y approaches infinity and perform a proper evaluation, which suggests that the integral likely converges.
Step-by-step explanation:
Convergence or Divergence of an Improper Integral
To determine whether the integral ₀∫[infinity] e−√y dy is convergent or divergent, we need to analyze the behavior of the integrand as y approaches infinity. Since the exponential function decays to zero as its argument goes to negative infinity, we expect the integral to be convergent. However, a proper evaluation through limit comparison or other tests is needed for a definite answer.
Convergence can be shown by taking the limit as b approaches infinity of the integral from 0 to b of the given function and checking if the result is finite. If we evaluate the integral ₀∫ e−√y dy as b approaches infinity, we see that the function e−√y becomes very small, suggesting that the integral is likely to converge.