In this question, you will estimate the value of the integral re & dx 3. [8/11 Points] DETAILS PREVIOUS ANSWERS For each of the following, enter your answers correct to two decimal places. using three different approximations. a. Find the area under the curve a. Subdivide the interval [1,4] into three su 1 = 5x- + 2 width and complete the following for x between 3 and 6. 20 - 1 (20) = 0.716531 Area - 321.00 21 - 2 ((al) = 1.026834 b. Find the area between the curve 2 82 - 3 ((ez) - 1.103638 y = 83 = 4 ((83) - 1.054389 and the x-axis for x between -5 and -3 X1 = 15 (x1) - 0.909796 Area - 1.02 X2 - 2.5 1( x2) - 1:086496 c. Find the area between the curve x3 = 35 ((x3) = 1.089911 1=x- 31 b. Calculate the approximate value of the integral using the trapezoidal rule. and the x-axis for x between 1 and 8. Area ~ 3.0159932 Area - 7 X d. Find the area bounded by the curves c. Calculate the approximate value of the integral using the midpoint rule. Area ~ 3.086203 y = 3x +1 d. Calculate the approximate value of the integral using Simpson's rule. and Area y = 3x + 1 e. It is possible to show that an antiderivative of x e"/3 is Area = 1.50 -3(x +3) es Using this antiderivative, calculate the exact value of the integral, Integral = 3.062837 4. [4/14 Points] DETAILS PREVIOUS ANSWERS Submit Answer The birth rate in a certain city is described by the following function b(t) = 8.48 - 0.04t 4. [2/4 Points] DETAILS PREVIOUS ANSWERS The city's death rate is given by d (t) = 4 +0.031 In this question, you will investigate whether the improper integral Here, t is measured in years, and t = 0 corresponds to the start of the year 1990. The birth and death rates are measured in thousands of births or deaths per year, At the start of 1990, the population of the city is 300 thousand. converges or diverges. If it converges, you will find its value. Enter all the following answers correct to two decimal places. a. Calculate the value of the integral a. Calculate the total number of births between the start of 1990 and the end of 1999. Number of births - 5.60 * thousand. b, Calculate the total number of deaths over the same period Number of deaths = 4.073 * thousand where b is a finite number whose value is greater than one . What is the population of the city at the start of year 2000? Value = Population : 299.20 * thousand. d. Considering just the period from the start of 1990 to the start of 2000, over what interval is the b. Does the value of the integral approach a limit as b tends to infinity? If so, enter this limiting value: (Enter your dates as years, not the number of years since 1990.) Increasing from 1990 until 1998 - 0 Over what interval is the population decreasing? Decreasing from 1998 / until 2000 symbolic formatting help e. Calculate the area between the curves y = b (( ) and y = d ( f ) for f between 0 and 10. Area : 21 47 Calculate the following integrals. If the answer requires a constant of integration, enter it as c. You may enter a symbo c answer for any of the following (for some, that means a formula in terms of x, for others, that means a formula for the exact answer) For those integrals that have a numerical answer, you may enter the numerical value of the integral as a decimal, but be sure to enter sufficiently many decimal places (enter as many as you can). = 1-2/x43 + c = 4in (5/2) + 4/3 154(3/2)] 9x 4exp ( - 1/4 ) + c ( 30-2 - 4 ) do = 6 (exp(-3/2) - exp(-1/2) - 4(3-1) x Your answer cannot be under