Q1

Consider the following. (a) Form the Integral that represents the area of the shaded region. g (Sum: (In) Find the area of the reglon. (Give an exact answer. Do not round.) Consider the following. (4, 16) f(x) = 16 15 10 5 g(X) = 8x- x- 2 X 4 6 8 (a) Form the integral that represents the area of the shaded region. dx (b) Find the area of the region. (Give an exact answer. Do not round.)Consider the following. 1 2 3 4 5 7 -2/ X - 6 -41 x - 6X -6 -8/ -10 (a) Find the points of intersection of the curves. (x, V ) = (smaller x-value) (x, y ) = (larger x-value) (b) Form the integral that represents the area of the shaded region. dx (c) Find the area of the shaded region. (Give an exact answer. Do not round.)Consider the following. y=x - 2x - X -4 - 2 2 4 -2 y = 2x -4 -6 (a) Find the points of intersection of the curves. (x, y) = ( (smallest x-value) ( x, y ) = ( x, y ) = (largest y-value) (b) Form the integral that represents the area of the shaded region. ax + dx (c) Find the area of the shaded region.Equations are given whose graphs enclose a region. Find the area of the region. (Give an exact answer. Do not round.) f(x) = x2 + 3; g(x) = -x4; x= 0; x=3Find the total income over the next 10 years from a continuous income stream that has an annual rate of flow at time t given by f(t) = 29,000e-01 (dollars per year). (Round your answer to the nearest cent.) $A franchise models the profit from its store as a continuous income stream with a monthly rate of flow at time t given by f(t) = 4000e0.005t (dollars per month). When a new store opens, its manager is judged against the model, with special emphasis on the second half of the first year. Find the total profit for the second 6-month period (t = 6 to t = 12). (Round your answer to the nearest dollar.)A continuous income stream has an annual rate of flow at time t given by f(t) = 12,000e0.02t (dollars per year). If money is worth 4% compounded continuously, find the function that gives the present value PV from 0 to t years. PV(t) = Find the present value of this stream for the next 8 years. (Round your answer to the nearest dollar.) $In this problem, p is In dollars and x is the number of units. Suppose the demand function for a product isp - i and the supply function ls p - 1 + 0.22:. [x + 1} Find the equilibrium quantity. x1 - Find the equilibrium point. {S ) Find the consumer's surplus under pure competition. {Round your answer to the nearest cent.) $