Evaluate each indefinite integral. 4x dx x^(-6) dx 5/x dx 22e^x dx 3/x dx (2e^x+8) dx

Evaluate each indefinite integral, using substitution when necessary. (4x+9)^3 (4) dx 2x(x^2+2)^8 dx x^9 e^(x^10 ) dx

The weekly marginal revenue from the sale of x pairs of tennis shoes is given by the equation below, where R(x) is the revenue in dollars. R^' (x)=38-0.03x+300/(x+1),R(0)=0 Find the revenue function. Find the revenue from the sale of 1000 pairs of tennis shoes, rounded to the nearest cent.

Calculate the following definite integrals by referring to the figure below with indicated areas. _a^bf(x) dx _a^cf(x) dx _c^df(x) dx _b^cf(x) dx

Evaluate each definite integral. _1^2x dx _2^38x^2 dx _2^36/x^2 dx _0^5e^2x dx _0^12x dx _5^91/(x-3) dx

Find the area bounded by the graphs of the indicated equations. y=-6x-7;y=0; -1x2 y=-x^2+30;y=0; -3x3 y=2x^2;y=18

Find the total income produced by a continuous income stream in the first 3 years if the rate of flow is given by the following function, where t is time in years. Round to the nearest cent. f(t)=400e^0.08t

A business is purchasing a piece of equipment that will produce a continuous income stream of income for 8 years with a rate of flow f(t)=9,000. If the continuous income stream earns 6.6%, compounded continuously, what will be the future value of the investment in 8 years? Round to the nearest cent.

Find the consumers' surplus and the producers' surplus at the equilibrium price level for the given price-demand and price-supply equations. Round all values to the nearest integer.

p=D(x)=70-0.07x p=S(x)=16+0.03x