MATH10560 Lecture 22: feb 27 2

1 pt) From Rogawski, Adams ET 3e section 5.2, exercise 13. Evaluate the integrals for f (r) shown in the figure below. The two parts of the graph are semicircles. 110 -1 a) 3f(x) dx = b) C 4f(x) dx = d) f , 2f(x) | dx =

T (10 points) 0 Given 4f() dx 8, f(x) dz valuate(2+f(x)) dr

Classification of s[(2)-modules We recall the standard basis for the Lie algebra s[(2) = s[(2, C), e = (0 0 1 0), h = (1 0 0 -1), f = (0 1 0 0), and the corresponding nontrivial commutation relations [h, e] = 2e, [h, f] = -2f, [e, f] = h.