Mathematica Homework #1

(1)  Here are some samples of indefinite and definite integrals.  Notice that in the second example we can give explicit limits to the integral in the form of variables.  In the third case we use NIntegrate, which gives us a numerical integral:

Integrate[Cosh[x], x]
Integrate[((N k T)/V), {V, V1, V2}]
NIntegrate[Exp[Sin[x]], {x, 0, 2  π}]

Please calulate the following integrals:

	(A)  Calculate the indefinite integral of (x^x).
	(B)  Integrate Log[x] from 1 to E.
	(C)  Log[1+ Sin[x]]  from 0 to 2π.

(2)  Plot the function Sin[Log[x]] from 1 to 100.

(3)  Plot the surface  z=Cos[x] Sin[y]  with x and y ranging from 0 to 4π.