Recall that if f is integrable on [a, b], then the Definite Integral of f from a to b is given by for any partition of [a, b] and any points xk . To simplify these calculations, we use equally spaced grid points and right Riemann sums. That is, for each value of n, we let AX* = Ax = = and Xk = a + kAx, for k = 1,2, ..., n. Then as n - co and A- 0, K= 1 [ f( ) dx = lim [ f ( xi ) Atx = lim. _ f(a + KAx ) Ax K= 1 In exercises #1-5, use the definition of the Definite Integral and right Riemann sums to evaluate the following definite integrals. Check your solutions using the Fundamental Theorem of Calculus. (1) j(x+ 3)dx (2 ) (2x - 4 ) dx (3) x2 dx ( 4) [ (-x3) dxx - 3 (15 ) (2 x 2 - 1 ) dx The following Sums will be of help. For n a positive integer and c a real number: c = cn KE1 K = n(n + 1) 2 K= 1 n k2 = n(n + 1)(2n + 1) 6 K= 1 n n2 (n + 1) 2 k3 = 4 K = 1