Find the area of the region bounded by the graphs of y = 16/x^2 + 5x + 6, y = 0,

Question

Find the area of the region bounded by the graphs of y = 16/x^2 + 5x + 6, y = 0, x = 0, and x = 4. A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet (0 lessthanorequalto x lessthanorequalto 4), where the variable force required is F(x) = 300 xe^-x pounds. Find the work done in pushing the block the full 4 feet through the machine. Round your answer to the three decimal places. Use a table of integrals to find the integral. integral squareroot 49 - x^4/x dx Find the area between the x-axis and the graph of the function y = 2/x^2 + 1. Suppose the capitalized cost C is give by C = C_0 + integral_0^pi c(t) e^-rt dt, where C_0 is the original investment, t is the time in years, r is the annual interest rate compound continuously, and c(t) is the annual cost of maintenance. Find the capitalized cost C of an assert forever if C_0 = 625,000,c(t) = 23,500(1+ 0.07 t), and r = 0.05. Round your answer to the nearest dollar.

Explanation / Answer

2)F(x)=3000xe-x

work done =[0 to 4]3000xe-x dx

integration by parts , u =3000x=>du =3000dx , dv =e-x dx =>v=-e-x

u dv =uv -vdu

work done =[0 to 4]3000x(-e-x) -[0 to 4]-e-x3000 dx

work done =[0 to 4]3000x(-e-x) -[0 to 4]3000e-x

work done =[0 to 4]3000x(-e-x) -[0 to 4]3000e-x

work done =[0 to 4]3000(-e-x)(x+1)

work done =[3000(-e-4)(4+1)]-[3000(-e-0)(0+1)]

work done =3000(1-(5/e4))

work done =2725.265 pound feet

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