Please help and show work, thank you

1. (10 pts) Use the limit process strategy to find the area of the region between the graph of the function f (x) = 3+4x-x2, [1,4]and the x-axis over the given interval. Conditions: f is continuous and nonnegative on closed [a, b]. A = limn-+0 Ek=1f(Ck)Ax where Ax = " and Ck = a + kAx. Strategy: a) Sketch the area b) Find Ax, k, f (Ck )and plug them into the sum. c) Evaluate the sum with respect to k. d) Evaluate the limit with respect to n. Page 1 of 3 2. (4 pts) Find dy / dx for y = dt tan .x 1+ 1 2 3. (4 pts) Evaluate [ 3x2 sin(x3) dx