Find the approximate distance traveled by finding the averag

Find the approximate distance traveled by finding the average of the under estimate and the over estimate. Time(sec) 0 2 4 6 8 Velocity(ft/sec) 20 30 38 44 48 Upper Sum =______Lower Sum =_____Average =_____For f(x) = squareroot 4-x^2 dx, find left hand sum on the interval [0,2] with n = 4 that approximates integral_0^2 squareroot 4 - x^2 dx. In the figure at the right find integral_-2^2 f(x) dx =_____integral_2^4 f(x) dx =____If the area of the shaded region is 1.5, find integral_-2^4 f(x) dx =_____

Solution

Time 0 2 4 6 8 Velocity 20 30 38 44 48 Time*vel 0 60 152 264 384 Left sum 476 Right sum 860 Average 668 f(x) =(4-x^2)^(1/2) Interval 0 2 n=4 x 0 0.5 1 1.5 2 f(x) 2 1.936492 1.732051 1.322876 0 x*f(x) 0 0.968246 1.732051 1.984313 0 Left sum 4.68461 Interval -2 2 x -2 -1 0 1 2 f(x) 0 -1 -1 -1 0 x*f 0 1 0 -1 0 Left sum