Hello, is chat gpt correct in this resolution and if so can u pls rewrite the answer thanks

8:03 all 5G Mail AA chat.openai.com C Integral calculation limitations. + To show that the equation [-oo+oof(x)dx=[-coOf(x)dx+ JO+cof(x)dx does not always hold for all functions f(x), we can provide a counterexample. Let's consider the function f(x) defined as: f(x) = 1 if x >=0 -1 if x co and y->-co of x - y: lim y->-co lim x->co (x - y) = too Since limy--co limx->co /yxf(t)dt is not equal to [-cotoof(x)dx for the function f(x) defined above, we have shown that the equation does not always hold for all functions f(x). Send a message. G Free Research Preview. ChatGPT may produce inaccurate information about people, places, or facts. ChatGPT Mar 23 Version m8:03 all 5G Mail AA chat.openai.com C Integral calculation limitations. + To calculate the integral Jyxf(t)dt, we first need to find the antiderivative of f(t). Since f(t) is not continuous at t=0, we need to split the integral into two parts: SyOf(t)dt + foxf(t)dt For the first integral, we have: SyOf(t)dt = Jyo(-1)dt = -y For the second integral, we have: SOxf(t)dt = SOx(1)dt = x Therefore, the integral Syxf(t)dt is equal to x - y. Now, let's calculate the limit of x->co and y->-co of X - y: lim y->-co lim x->co (x - y) = too Since limy->-co limx->co /yxf(t)dt is not equal to [-oo+cof(x)dx for the function f(x) defined above, Send a message. G Free Research Preview. ChatGPT may produce inaccurate information about people, places, or facts. ChatGPT Mar 23 Version