Calculus 1 1 True or False (1) f(x)= ) 1,xis rational 0,xis irrational is integrable on any bounded closed interval [a,b] (2)The derivative of y=y(x) determined by the formula arctan(y)/(x)=lnsqrt (x^2+y^2) is y'=(x+y)/(x-y)

Let's analyze each statement one by one:(1) The function is not integrable on any bounded closed interval . This is because the function is not continuous on the interval, as it jumps between two different values at each irrational and rational point. For a function to be integrable, it must be continuous on the interval.(2) To find the derivative of determined by the formula , we need to differentiate both sides of the equation with respect to . Differentiating the left side with respect to gives us . Differentiating the right side with respect to gives us . Simplifying the right side, we get . Therefore, the derivative of determined by the formula is .