高分求用Maple做一道微积分的题!
题目
高分求用Maple做一道微积分的题!
Consider the following function on the interval [0, π/2].
f (x) = √ 2x cos8(2x)
(a用中线方法求方程下方区域) Approximate the area under f (x) on the given interval using midpoints（中点） with n = 10.
(b求定积分) Compute the definite integral of f (x) on the interval [0, π/2].
(c求绝对误差) Find the absolute value of the error involved in approximating the area under f (x) on the given interval using a Riemman sum with midpoints and n = 10.
(d) Using trial and error,determine the smallest number n of subintervals such that the absolute error of the midpoint Riemann sum with respect to the exact value of the area is less than 0.0005.
方程式 根号下2x乘以 (cos(2x))^8
Consider the following function on the interval [0, π/2].
f (x) = √ 2x cos8(2x)
(a用中线方法求方程下方区域) Approximate the area under f (x) on the given interval using midpoints（中点） with n = 10.
(b求定积分) Compute the definite integral of f (x) on the interval [0, π/2].
(c求绝对误差) Find the absolute value of the error involved in approximating the area under f (x) on the given interval using a Riemman sum with midpoints and n = 10.
(d) Using trial and error,determine the smallest number n of subintervals such that the absolute error of the midpoint Riemann sum with respect to the exact value of the area is less than 0.0005.
方程式 根号下2x乘以 (cos(2x))^8
答案
要使绝对误差小于 0.0005,从以上试算结果可以看出,n 的最小值等于 5
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