Show transcribed image text Consider the area bound by the curves y a) Without plotting these functions, determine where they intersect. Show your worlk. b) Now use Desmos or some other plotting program to graph the two functions. If you want 5. x2e_x and y = xe-z to find the area bound by these curves, is it easiest to integrate with respect to x or y? Include a plot of the two functions and use the graph to help justify your answer. e) If integrating with respect to x, which curve lies above the other on your integration interval? If integrating with respect to y, which curve lies to the right of the other on your integration interval? Show a calculation that backs up your answer. You may not justify your answer by referring the plot of the functions (since you won't be able to do this on exams). d) Calculate the area between these two curves. Show your work. 6. A rocket accelerates by burning its onboard fuel, so its mass decreases over time. Suppose the initial mass of the rocket at liftoff (including fuel) is mo, the fuel is consumed at a constant rate, r, and the exhaust gases are ejected with constant velocity, Ve, relative to the rocket. A model for the rocket's velocity as a function of time is given by the equation: mo -rt v(t)gt – veIn mo The constant g corresponds to the acceleration of gravity at the earth's surface. If we let y = 0 m correspond to the surface of the earth and +y be upward, find the height of the rocket one minute after lift off. Here are values for the constants but do not plug these numerical values in until after you have evaluated all integrals and have solved for the rocket height after one minute: g = 9.8 m/s2, Ve = 3000 m/s, mo = 30,000 kg, and r = 160 kg/s.