Question 1:

The rate (in liters per minute) at which water drains from a tank is recorded at half-minute intervals, Use the average of the left- and right-endpoint approximations to estimate the total amount of water drained during the first 3 min. t min 0 0.5 1 1.5 2 2.5 3 1/min 48 46 44 42 40 38 36 Answer: liters.The rectangles in the graph below illustrate a left endpoint Riemann sum for f(@) = 6 - + 2: on the interval [4, 8]. The value of this left endpoint Riemann sum is 23.07, and it is there is ambiguity the area of the region enclosed by y = /(+), the x-axis, and the vertical lines x = 4 and x = 8. Left endpoint Riemann sum for y = =: + 2x on [4, 8]The rectangles in the graph below illustrate a right endpoint Riemann sum for f () = 6 + 2x on the interval [4, 8]. The value of this right endpoint Riemann sum is 23.08 and it is an there is ambiguity the area of the region enclosed by y = f(x), the x-axis, and the vertical lines x = 4 and x = 8. Right endpoint Riemann sum for y = = + 2x on [4, 8]Using left and right Riemann sums based on the diagrams above, we definitively conclude that 2 6 6 + 2x dx O - 2 6 Hint: For the last integral, you should consistently choose either to underestimate or overestimate the area. This may require that you use the left Riemann sum for some x- intervals and the right Riemann sum for other x-intervals