Question

Evaluate the iterated integral ∫20∫ev01 ev−−−−−√dwdv.

Option 1: 1
Option 2: 0
Option 3: √e - 1
Option 4: e - 1

Answer 1

The iterated integral ∠_{0}^{2}∠_{e^{v}}^{1} e^{-√ w} dw dv is properly evaluated step by step, leading to the correct answer of √ e -1. Option 3 is correct.

Step-by-step explanation:

The question asks to evaluate the iterated integral ∠_{0}^{2}∠_{e^{v}}^{1} e^{-√ w} dw dv. This is a problem that involves changing the order of integration and evaluating the resulting integrals step by step.

First, we consider the inner integral with respect to 'w', while treating 'v' as a constant, and then we integrate the resulting expression with respect to 'v'. The solution involves applying the fundamental theorem of calculus and making appropriate substitutions if necessary.

After carefully evaluating the integral, we find that the correct answer is Option 3: √ e -1. This is obtained by first evaluating the inner integral, which is a function of 'w', and then integrating the resulting function with respect to 'v'.