1. Improper Integrals both a and b

2. (Newton's Law of Heating) Newton's Law of Heating is one of the most important differential equations in the study of thermodynamics and heat propagation. At its basic form, Newton's law of heating is given by the equation of " = k . (Tor Tm), where T is the temperature of an object, Tm is the ambient temperature of the object, over a measurement of time t. a. Let C 0 be any constant value. Verify that T (() = Geff + 7,,, is a solution of Newton's Law of Heating. Assume Tm is a constant unknown value. b. The value C in the equation T(t) above is defined by the difference between the initial temperature and the ambient temperature of the object. Suppose an object, with an initial temperature of 300 F, is removed from a furnace and placed into a room with an ambient temperature of 70 F Three minutes later, the temperature is 200 F How long will it take for the object to get to 100 F: Hint solve for k firstEvaluate the following integrals. Make sure to show the factorization of the denominator. In(x) dx red dx X