The average value of f over the region R becomes favg=1A(R)∬Rf(x,y)dA Here, A(R) denotes the area of the region R. Answer and Explanation: We wish to compute the average value of f(x,y)=x2+y2 over {eq}R=\lef...
f_( (ave ))=1(A(R)) _R f(x, y) A=1(10) ∫_0^5 ∫_(-1)^1 x^2 y x y=1(10) ∫_0^5[13 x^3 y]_(x=-1)^(x=1) y=1(10) ∫_0^5 2(3) y (d) y=(1)(10)[(1)(3) y^(2)]_(0)^(5)=(5)(6)....
Average Value: The average value of a function f(x,y) over a region D having area Ad is defined by the double integral {eq}\displaystyle M = \frac{1}{A_d} \iint_D f(x, y) dx dy {/eq} The integral is evaluated in rectangular coordin...
f(x,y)=e^y√ (x+e^y), R=[0,4]* [0,1] 相关知识点: 试题来源: 解析 3.327 A(R)=4⋅ 1=4,50, so (split)∫_((ave))&=1(A(R))_Rf(x,y)=14∫_0^4∫_0^1e^y√(x+e^y) \ \ =14∫_0^4[23(x+e^y)^(3/(2))]_(y=0)^(y=1)\ (d)x & =(1)(4)...
James Stewart《微积分》笔记·6.5 Average Value of a Function(函数的平均值) JackLin Lūcem sequor. 来自专栏 · James Stewart《微积分》笔记 11 人赞同了该文章 一、函数的平均值 求连续函数 y=f(x), a≤x≤b 的平均值: 将区间 [a,b] 分为n 个相等的子区间,各个子区间的长度为 Δx=b−an ...
Question: Find the average value of f over the given rectangle. f(x,y)=4eyx+ey,R=[0,14]×[0,1]favg=(∫0∫014eyx+eydydx= Show transcribed image text There are 2 steps to solve this one. Solution Share Answered by Calculus expert1292...
The average value of function( f) over the interval( [a,b]) is defined as ( A(y)=1/(b-a)(∫ )_a^bf(x)dx). ( A(y)=1/(b-a)(∫ )_a^bf(x)dx) Substitute the actual values into the formula for the average value of a function. ( A(y)=1/(2-0)((∫ )_0^...
30、需求的交叉弹性(Cross elasticity of demand) 需求的交叉弹性是指商品Y的价格发生1%的变化时所引起的商品X的需求量变化的百分比。 31、垄断的无谓损失(Deadweight loss of monopoly) 如果一个完全竞争的市场转变为一个垄断的市场,这种转变所带来的总剩余...
结果1 题目 Find the average value of$$ f ( x , y ) = x + 2 y $$over the rectangle$$ R = \left\{ ( x , y ) | 0 \leq x \leq 2 , 0 \leq y \leq 1 \right\} $$ 相关知识点: 试题来源: 解析 2 反馈 收藏 ...
Average Value of a Functionf(x,y) To determine the average value of a function f(x,y) integrate the following {eq}\displaystyle f_{ave} = \frac{1}{A(R)} \iint_{R} f(x,y) \ dA {/eq} where A(R) denotes the area of the region enclosed by ...