Calculus UNIT503A: What About Volume?

2745 days ago by MATH4R2013

#7 p411: consider the region bound by the lines x+2*y==2, x==0, y==0 #7 p411: find the volume of revolution of the this region about the x-axis var('y') show(solve(x+2*y==2,y)) show(integrate(pi*(-x/2+1)^2,x)) show(integrate(pi*(-x/2+1)^2,x,0,2)) show(integrate(pi*(-x/2+1)^2,x,0,2).n()) plot([-x/2+1],0,2) 
       




#11 p411: consider the region bound by the curve y==x^2 and the lines x==2, y==0 #11 p411: find the volume of revolution of the this region about the x-axis show(integrate(pi*(x^2)^2,x)) show(integrate(pi*(x^2)^2,x,0,2)) show(integrate(pi*(x^2)^2,x,0,2).n()) plot(x^2,0,2) 
       



#13 p411: consider the region bound by the curve y==sqrt(9-x^2) and the line y==0 #13 p411: find the volume of revolution of the this region about the x-axis show(integrate(pi*(9-x^2),x)) show(integrate(pi*(9-x^2),x,-3,3)) show(integrate(pi*(9-x^2),x,-3,3).n()) plot(sqrt(9-x^2),-3,3) 
       



#15 p411: consider the region bound by the curve y==x^2+1 and the line y==x+3 #15 p411: find the volume of revolution of the this region about the x-axis show(solve(x^2+1==x+3,x)) show(integrate(pi*(x+3)^2,x)-integrate(pi*(x^2+1)^2,x)) show(integrate(pi*(x+3)^2,x,-1,2)-integrate(pi*(x^2+1)^2,x,-1,2)) show(integrate(pi*(x+3)^2,x,-1,2).n()-integrate(pi*(x^2+1)^2,x,-1,2).n()) plot([x^2+1,x+3],-1,2)