Question

a. For each of the following, answer correct to two decimal places

Find the area under the curve y=3x^3+2

Find the area between the curve y=2/x and the x-axis for x between -5 and -4

Find the area between the curve y=x^2-3x and the x-axis for x between 2 and 7

Find the area bounded by the curves y=6x^3+1 and y=6x+1

b. The birth rate in a certain city is described by the following function

. The city's death rate is given by . 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. Answer the following correct to two decimal places.

Calculate the total number of births between the start of 1990 and the end of 1999. (in thousands)

Calculate the total number of deaths over the same period (in thousands)

What is the population of the city at the start of year 2000? (in thousands)

Considering just the period from the start of 1990 to the start of 2000, over what interval is the population increasing? (not the number of years since 1990)

Over what interval is the population decreasing?

Calculate the area between the curves y = b ( t ) and  y = d ( t ) for t between 0 and 10.

Answer 1