Integration, Maclaurin series, and radioactivity

integrate:-

1. integral (4x-x^2) ^ (1/2)from 0 to 4

i know that I should use completing the square

so i ended up with (-4-(x-2)^2)^(1/2)

however, it doesn't look right to me, May I get a helpful solution?

2.

A certain radioactive isotope is observed to decay to 98% of its initial amount over a

period of one year.

a) Assume that the sample has an initial mass of 100g. Find a function that represents

the mass of a sample as a function of time (in years).

b) What is the half-life of the isotope?

c) How long will it take the sample with initial mass of 100g to decay to a mass of 8g?

3.

Find the Maclaurin series for the functions sinh(

x) and cosh(x) by using the Maclaurin

series for ex and the de nitions of sinh(x) and cosh(x) in terms of ex. Compute the radius

of convergence for each series.