Section 15.3 (6th edition): Exercise 8: Evaluate the double integral

'integrate('integrate(y/(x^5+1),y,0,x^2),x,0,1);

integrate(integrate(y/(x^5+1),y,0,x^2),x,0,1);

Exercise 12: Evaluate the double integral

'integrate('integrate(x*sqrt(y^2-x^2),x,0,y),y,0,1);

assume(y > 0);

integrate(integrate(x*sqrt(y^2-x^2),x,0,y),y,0,1);

Exercise 14: Evaluate the double integral

'integrate('integrate(x+y,y,x^2,sqrt(x)),x,0,1);

assume(x > 0);

integrate(integrate(x+y,y,x^2,sqrt(x)),x,0,1);

Exercise 18: Evaluate the double integral

'integrate('integrate(2*x*y,y,h(x),k(x)),x,0,1);

h(x) := 2*x;

k(x) := 3 - x;

integrate(integrate(2*x*y,y,h(x),k(x)),x,0,1);