Integral Calculus Answers

INTEGRATE : (1/x)(sin((1/x)-x)) with limits 1/3 to 3

How to integrate square root of tan x?

find the difinite integral from zero to infinity x^3/e^x-1dx

If an investment promises to provide A dollars at time t in the future, we can de fine the
present value P as the amount that would have to be invested to generate A dollars after
time t, assuming an interest rate r. This can be expressed as Pe^(rt) = A, or P = Ae^(-rt). The
capital value of an asset can be de fined as the present value of all future income from that
asset. If the asset lasts inde finitely, the capital value can be written as
CV=∫(lower limit:0,upper limit:infinity) K(t)e^(-rt)dt,
where K(t) is the annual rate of income from the asset, r is the annual rate of interest, and
t is the time in years.
Suppose I sell the mining rights to a piece of land to a company for a payment of 10000e^(0.04t)
dollars per year. Find the present value of this income, assuming interest of 12% annually

Integrate E^(Sqrt[x])

solve indefinite integral from -1 to 1 (1-x)dx?

slove dy/dx= x-e^x

A right circular cone is cut in half .The diameter of the base is 2r and the perpendicular height is h, By considering the volume of one slice of the half cone, and then summing all such slices, show from first principles that the volume is 1/6pi r^2h

find the area bounded by the y² = 2x, y = x - 4.

Given the marginal cost function C'(x)= 0.4x-60 and that the cost of producing 100 items is $4350

Find the cost function