#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)
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#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)
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#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)
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#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)
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