clc, clear all
format long
%% part a
syms x y
I=int(int(log(y*y*x)*cos(exp(x^(1/2)))/(x*x*y*y*y+5),x,y,-y*y+4*y-2),y,1,2);
% We have obtained an analytical result. I is a symbolic number.
If=double(I) % Converting I to double-precision floating-point number
%% part b
% change variables to use integral2 function
f = @(x,y) log(x.^2.*y).*cos(exp(y.^(1/2)))./(y.^2.*x.^3+5);
ymin=@(x) x;
ymax=@(x) -x.^2+4*x-2;
xmin=1;
xmax=2;
In=integral2(f,xmin,xmax,ymin,ymax,'Method','iterated')
