Answers by visitors named: SOmeone

YES AHMED I DO

A = 0.5(b1 + b2)h h = dx so the change in x A = 0.5(v(0) + v(0.3))(0.3 - 0) + 0.5(v(0.3) + v(1))(1 - 0.3) + 0.5(v(1) + v(1.6))(1.6 - 1) + 0.5(v(1.6) + v(2))(2 - 1.6) A = 0.5(0 + 24.5)(0.3) + 0.5(24.5 + 27.8)(0.7) + 0.5(27.8 + 28.3)(0.6) + 0.5(28.3 + 29.0)(0.4) A = 3.675 + 18.305 + 16.83 + 11.46 A = 50.27 feet The car covered approximately 50.27 feet during those 2 minutes.

Q1: There are three intersection points: (-1,1), (0,0), (1,-1) Thus the endpoints are: (-1,1), (-0.5,0.5), (0,0), (0.5,0.5), (1,1) Thus, the midpoints are: (-0.75,0.75), (-0.125,0.125), (0.125,-0.125), (0.75,-0.75) The area is as follows: 0.75(-0.5) + (0.25(-0.5)) + -0.25(0.5) + -0.75(0.5) = -1 I took the area of the whole thing instead of taking the area of the 2 regions separately because I assumed that is what the question is asking Q2: If we evaluate the derivative of the function, we get: int of [ln(t)] from 2x to 5x which results in ln|5x| - ln|2x| Taking the derivative of this, we get: d/dx (ln(5|x|) - ln(2|x|)) d/dx (ln(5|x|/2|x|)) d/dx (ln(5/2)) This equals 0 Since the derivative of a function gives the slope of the tangent line at any given point, we know the above function is constant on the given interval because the derivative is 0 which indicates the function neither decreases nor increases which means it remains constant