Write the integral with the order of integration reversed (changing the limits of integration as necessary).

Question

Quizplus · Accepted Answer

Since we are reversing the order of integration, we need to switch the limits of integration and then switch the order of the variables. The given integral is written as:

$\int_0^1\int_0^{\ln(1+x)}f(x,y)dydx$

To reverse the order of integration, we write the integral as:

$\int_0^{\ln(2)}\int_{e^y-1}^1f(x,y)dxdy$

We can see that the limits of integration have been reversed and the order of variables has been switched from $x$ and $y$ to $y$ and $x$.

Thus, the answer is D.

Write the Integral with the Order of Integration Reversed (Changing