Question

Determine whether the integral is convergent or divergent. ∫[infinity]​₀ e⁻√ʸ dy

O convergent
O divergent
If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.)

Answer 1

The integral ∫∞​​​0 e-√y dy is convergent and its value is 1.

Step-by-step explanation:

The integral ∫∞​​​0 e-√y dy can be determined to be convergent or divergent by evaluating the limit of the function e-√y as y approaches infinity. Since the exponential function tends to zero as the argument approaches infinity, the integral is convergent.

To evaluate the integral, we can use the rule that the integral of e-x dx is equal to -e-x + C. Applying this rule to our integral, we get:
∫∞​​​0 e-√y dy = - e-√y|0∞ = -0 - (-e0) = 1