Question

Calculate the iterated integral.

Answer 1

Step 1:

The iterated integral is.

Fubinis theorem :

.

The iterated integral can be written as.

First integrate with respect to , holding as a constant.

Consider .

Change in integral limits :

lower limit : if v = 0 then t = u.

Upper limit : if v = 1 then t = u + 1.

Substitute and in the iterated integral.

.

Solution :

.