Question

Consider the integral 2 to 5 sqrt(1+sin^2x) dx, which can't be evaluated exactly. f(x) <=1.5 , f'(x) <=0.5 , f''(x) <= 1 , f'''(x) <= 2 , f''''(x) <= 8 , if x is between 2 and 5, and f(x) = sqrt(1+sin^2x). a: Determine the smallest value of n which guarantees that the trapezoid approximation will
be within 10−3 of the actual value of integral 2 to 5 sqrt(1+sin^2x).