Integral Calculus Answers

am stuck with this question:

f belongs to L1(0,infinity)

want to prove lim_t->infinity 1/t^2* interal{0 to t }x^2 *f(x)dx=0

∫∫∫2y2z dxdzdy ?
∫∫∫dzdxdy ?

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])