Answer to Question #188844 in Calculus for Sarita bartwal

Question

The function,

f(x,y)= { x ; y is rational

{ 0 ; y is irrational

is integrable or not

True or false with full explanation

Answer 1

Solution:-

Given that f(x,y) = {x ; his rational }.and {0;y is irrational}

In this case we can see that

Function must be integrable

As any function of x and y , and x is dependent on value of x , in this case x is defined when y is rational .

And x is 0 in case of y is irrational.

When x is defined in the domain and y is rational or irrational than the function must be integrabal ,

The condition is -f(x,y) , is defined in the domain , for both x and y .

Then overall function is integrable.