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Evaluate the following integral. int x cos x dx Evaluate the definite integral below. Evaluate the following integral. int sin2 x cos 2 x: dx Given the function of the curve below, find the volume of the solid generated by rotating the area (A ) about the x-axis. f(x) = In x 1 le x le 3 Newton's Law of Heating and Cooling gives the model below. For water, k = -0.04095. Assume that you are in a 76 degree F room with a cup of water. The water temperature is 34.3 degree F. Find the water temperature in the cup after 10 minutes. T = A+Sekt

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1 pt) Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose t is time, T is the temperature of the object, and Ts is the surrounding temperature. The following differential equation describes Newton's Law

dT/dt=k(T-Ts),

where k is a constant.

Suppose that we consider a 92(oC)cup of coffee in a 24(oC) room. Suppose it is known that the coffee cools at a rate of 2(oC)/min. when it is 70(oC). Answer the following questions.

Find the constant k in the differential equation.
Answer (in per minute): k=

2. What is the limiting value of the temperature?
Answer (in Celsius): T=

3. Use Euler's method with step size h=2 minutes to estimate the temperature of the coffee after 10 minutes.
Answer (in Celsius): T(10)?

Am sorry to ask a lot f questions today