Calculate the L4 approximation for f(x) = cos2xon [pi/4,pi/2](Round your answer to four decimal places.) . Solution We divide the interval [pi/4, pi/2] into 4 subintervals of equal length, ?x = ((pi/2)?(pi/4))/4 = pi/16. This divides the interval into 4 subintervals each with length ?x = pi/16. We label the endpoints of these subintervals as x0 = pi/4, x1 = 5pi/16, x2 = 6pi/16 = 3pi/8, x3 = 7pi/16, x4 = 8pi/16 = pi/2. L4 is called the left endpoint approximation or the approximation using left endpoints (of the subintervals) and 4 approximating rectangles. so, L4 = [f (x0) + f (x1) + f (x2) + f (x3)].