Let .G; / be a group and suppose H is a nonempty subset of G. Prove that .H; / is a subgroup of .G; / provided that H is closed under and that for every g 2 H, we have g 1 2 H. This gives an alternative proof strategy to Proof Template 24. You do not need to prove that e 2 H. You need only prove that H is nonempty. 42.

L35 - 15 Now You Try It (NYTI): 1. Evaluate each integral. ▯ √ (a) 2x 4 − 2xdx ▯ e2x (b) dx e +1 2. Evaluate the deﬁnite integrals. ▯ 4 − x (a) √ dx 1 x ▯ π/2 sin(t) (b) 1+cos 2(t)dt 0