下面是它的代数表达式：J(x)=Li(x)-\sum_{\rho}Li(x^{\rho})-\ln 2 +\int_x^\infty\frac...
RiemannSum(f(x), x = a..b, opts) RiemannSum(Int(f(x), x = a..b), opts) Parameters f(x) - algebraic expression in variable 'x' x - name; specify the independent variable a, b - algebraic expressions; specify the interval opts - equation(s) of the form option=val...
A sum of this form is called a Riemann sum, named for the 19th-century mathematician Bernhard Riemann, who developed the idea.Definition Let f(x)f(x) be defined on a closed interval [a,b][a,b] and let PP be a regular partition of [a,b][a,b]. Let ΔxΔx be the width of ...
Riemann sum, Simpson’s. Back to Top Example Problem (Right Hand Riemann) Example problem:Find the area under the curve from x = 0 to x = 2 for the function x3using the right endpoint rule. Step 1:Sketch the graph: Step 2:Draw a series of rectanglesunder the curve, from the x-axi...
黎曼(Riemann)对定积分的定义是：积分区间划分为无数子区间，子区间内任意一点的函数值乘以子区间的长度...
Riemann first observed that on the assumption that the infinitesimal measuring rod may be put anywhere, and so space has everywhere constant curvature, then the sum of the angles in a triangle is known once it is known in a single triangle. Riemann had no problem accepting the geometry on a...
RiemannSum(Int(f(x), x = a..b), method = midpoint, opts) Parameters f(x) - algebraic expression in variable 'x' x - name; specify the independent variable a, b - algebraic expressions; specify the interval opts - equation(s) of the form option=value where option is one...
The RiemannSum(f(x), x = a..b, method = left, opts) command calculates the left Riemann sum of f(x) from a to b. The first two arguments (function expression and range) can be replaced by a definite integral. • If the independent variable can be uniquely determined from the ...
Endpoints, number of intervals, and method 2 left endpoint left endpoint 3 a=−1 −10 10 4 right endpoint right endpoint 5 b=3 −10 10 6 number of intervals number of intervals 7 n=12 −10 100 8 choice of method: set c=0 for left-hand sum, c=1 for right-hand sum, c=...
A Riemann sum is an approximation of the area under a mathematical curve between two X values. This area is approximated using a series of rectangles that have a width of delta X, which is chosen, and a height that is derived from the function in questio