Question

1. Consider the function [ F(x)=int_{0}^{x} frac{1}{1+t^{2}} d t+int_{0}^{1 / x} frac{1}{1+t^{2}} d t ] (a) Using the Second Fundamental Theorem of Calculus, show that ( F(x) ) is constant on ( (0, infty) ) and on ( (-infty, 0) ) (b) Find the constant value(s) of ( F(x) ). (You don't need the Second Fundamental Theorem for this. Just think about what it means for ( F(x) ) to be constant on an interval.)

          1. Consider the function
[
F(x)=int_{0}^{x} frac{1}{1+t^{2}} d t+int_{0}^{1 / x} frac{1}{1+t^{2}} d t
]
(a) Using the Second Fundamental Theorem of Calculus, show that ( F(x) ) is constant on ( (0, infty) ) and on ( (-infty, 0) )
(b) Find the constant value(s) of ( F(x) ). (You don't need the Second Fundamental Theorem for this. Just think about what it means for ( F(x) ) to be constant on an interval.)

$1. Consider the function [ F(x)=int0^x frac11+t^2 d t+int0^1 / x frac11+t^2 d t ] (a) Using the Second Fundamental Theorem of Calculus, show that ( F(x) ) is constant on ( (0, infty) ) and on ( (-infty, 0) ) (b) Find the constant value(s) of ( F(x) ). (You don't need the Second Fundamental Theorem for this. Just think about what it means for ( F(x) ) to be constant on an interval.)$

Added by Tyler R.

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