Using simpson 1/3 rule for double integration I want to give first only y limit then after getting this integration I want to give x limit f(x,y)=sin(x)(A1sinh(y)+B1sinh(b-y))+ C1sin(x)sinh(b-y)+D1sin(x)sinh(y)+E1sinh(Lx)* sin(y)+sinh(x)*sin(y)

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NILESH PANDEY 2015-11-1

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https://ww2.mathworks.cn/matlabcentral/answers/252139-using-simpson-1-3-rule-for-double-integration-i-want-to-give-first-only-y-limit-then-after-getting-t

编辑： Torsten 2015-11-9

is there a method in simpson 1/3 rule for double integration that first i give only y limit after getting this integration i give x limit and function has both x and y variable in multiplication so i cant use simpson 1/3 rule for single integration i am using a simpson 1/3 rule for double integration the code but in this code i have to give x and y limit both at a same time the code is

 syms x y;
f = inline(f(x,y));
c = inline('1');
d = inline('2');
a =0; 
b = x;
m = 4;
n = 4;
hx = (b-a)/n;
An = 0;
Ae = 0;
Ao = 0;
for i = 0:n
x = a + i*hx;
ya = c(x);
yb = d(x);
hy = (d(x) - c(x))/m;
Bn = f(x,ya) + f(x,yb);
Be = 0;
Bo = 0;
for j = 1:m-1
y = ya + j*hy;
z = f(x,y);
if rem(j,2)==0
Be = Be + z;
else
Bo = Bo + z;
end
end
A1 = (Bn + 4*Bo + 2*Be)*hy/3;
if i == 0 | i == n
An = An + A1;
else
if rem(i,2)==0
Ae = Ae + A1;
else
Ao = Ao + A1;
end
end
end
Dint = (An + 4*Ao + 2*Ae)*hx/3;
end

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Torsten 2015-11-2

is there a method in simpson 1/3 rule for double integration that first i give only y limit after getting this integration i give x limit

Why do you want to do this ?

Best wishes

Torsten.

NILESH PANDEY 2015-11-4

file.pdf

because in my integration problem first i have to integrate w.r.t. y than after getting this i have to integrate dx/f(x) so if i give both x and y limit at same time it will integrate w.r.t x also to clarify this i am attaching a file i hope this will help

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Answer 1

Torsten 2015-11-4

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/252139-using-simpson-1-3-rule-for-double-integration-i-want-to-give-first-only-y-limit-then-after-getting-t#answer_198430

Write down the Simpson-rule approximation for

integral_{y=c}^{y=d) exp(f(x,y)) dy .

This will be a finite sum including the variable x. Call it sum(x).

Thus under the first integral you have an expression of the form 1/sum(x) to integrate over [a:b].

Now apply Simpson's rule again in x-direction.

Best wishes

Torsten.

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NILESH PANDEY 2015-11-7

编辑：NILESH PANDEY 2015-11-7

sir i cant understand it what is I(x) and result = simpson(@(x)I(x),a,b,deltax) what is the meaning of result and simpson. and is there a difference in answer if i use this q = integral(fun,xmin,xmax) not simpson 1d code