Key to MATLAB Exercise 7 School of Mathematical Sciences Xiamen Univer http:/edjpkc.xmu.ed > clear; syms x y f, fsin(y)/(x 2*y+1); > int(f, x, -inf, inf ans pi*sin(y/y(1/2) > clear; syms x y f; fsin(y)/(x2 y+1) >>int(int(f, x, -inf, inf), -inf, inf) ans > clear; syms x f, fx2+ >>f int diff=int(diff(f)) f int diffe >>f diff int=diff(int(f)) f diff int= x^2+1 diff(int(f)) is not equal to int(difi(f)), the difference between them is the constant item C >> clear > simplify(symsum(k 3, 1,n)) 1/4*n^4+1/2*n^3+1/4*n^2 > clear; syms k; >> symsum(1/(k^2-1),1,nf) m(1/(k2-1)k=1…Int) > symsum(1/(k 2-1), 2, inf) ans > clear; syms kx f; fk xk; > symsum(f, k, 1, inf) x*(x+1)/(x-1)~3 > clear; syms x f, fexp(2x) > taylor(f, 15) ans Ex7-5Key to MATLAB Exercise 7  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Key to Ex7­5  >> clear; syms x y f; f=sin(y)/(x^2*y+1);  >> int(f,x,­inf,inf) ans =  pi*sin(y)/y^(1/2)  5) >> clear; syms x y f; f=sin(y)/(x^2*y+1);  >> int(int(f,x,­inf,inf),­inf,inf) ans =  0  9.  >> clear; syms x f; f=x^2+1;  >> f_int_diff=int(diff(f)) f _int_diff=  x^2  >> f_diff_int=diff(int(f)) f_diff_int =  x^2+1  diff(int(f)) is not equal to int(diff(f)), the difference between them is the constant item C.  10.  1) >> clear; syms k n;  >> simplify(symsum(k^3,1,n)) ans =  1/4*n^4+1/2*n^3+1/4*n^2  2) >> clear; syms k;  >> symsum(1/(k^2­1),1,inf) ans =  sum(1/(k^2­1),k = 1 .. Inf) 3) >> clear; syms k;  >> symsum(1/(k^2­1),2,inf) ans =  3/4  4) >> clear; syms k x f; f=k^2*x^k;  >> symsum(f,k,1,inf) ans =  ­x*(x+1)/(x­1)^3  11.  1) >> clear; syms x f; f=exp(2*x);  >> taylor(f,15) ans =