Help With Integrating a function with certain bounds

So here is my code:

%% Givens
P1= 160; %kpa
P2= 500; %kpa
P3= P2; %kpa
Mg= 2; %kg
Mf= 1; %kg
Mt= 3; %kg
syms V1 V2
V3=1.2*V1; %m^3
V3=1.2*V1==V2; %m^3
%% Part A
%Table A-5 %
Pa=160;
Pl= 150;            Ph= 175;            P2= 500;
vfl= 0.001053;      vfh= 0.001057;      vf2= 0.001093;
vgl= 1.1594;        vgh= 1.0037;        vg2= 0.37483;
Tl= 111.35;         Th= 116.04;         T_500= 151.83;

%Table A-6
P2= 500;
Tl2= 600;           Th2=700;
vl2= 0.80409;       vh2= 0.89696;

% To test if state '2' is in vapor or staurated
Vfa= ((vfh-vfl)/(Ph-Pl))*(Pa-Pl)+vfl;
Vga= ((vgh-vgl)/(Ph-Pl))*(Pa-Pl)+vgl;
X=Mg/Mt;
v1=Vfa+X*(Vga-Vfa);
V1=v1*Mt;
V3=1.2*V1;
V2=V1;
v2=V1/Mt;
v3=V3/Mt;

if X<1;   
T1= ((Th-Tl)/(Ph-Pl))*(Pa-Pl)+Tl
end

if v2>vg2
    T2= ((Th2-Tl2)/(vh2-vl2))*(v3-vl2)+Tl2
else T2=T_500
end
%% Part B
if v2>vg2
    Mf=0
end
%% Part C
for P=P1; 
    V_1=V1;  V_2=V2;
    fun= @(V) P.*V;
    Work_12= integral(fun,V_1,V_2)
end
for P=P2;
    V_2=V2;  V_3=V3;
    fun=@(V) P*V;
    Work_23= integral(fun,V_2,V_3)
end
Work_total=Work_12+Work_23

    

Everything works, except the final part "Part C"

For Work_23, I need to take the integral of 'P dV' with the bounds being V2 and V3. Basically once integrated I need it to look like P2(V3-V2) and im expecting an answer of 219.xxx however its giving me 530.xxx. Can someone please help

Answer 1

[Walter Roberson]

    fun=@(V) P*V;

The indefinite integral of a*x is 1/2*a*x^2 so the definite integrap from b to c would be 1/2*a*(c^2-b^2)

Basically once integrated I need it to look like P2(V3-V2)

That is something that would happen if you were doing not

[Areg Arzoomanian]

so if i wanted to make it P2dV how would I change my code?

[Walter Roberson]

    fun=@(V) P*ones(size(V));

The ones() is important for integral(): integral() will pass in a vector of V values and needs something the same size as V in return.