8 solids of revolution

Question 1

revolution around x axis

Answer 1

v= b—->a piy^2 dx

Question 2

revolution around y axis

Answer 2

v= d—->c pix^2 dy

Question 3

y= sqrrt(1+x/x)

b=4
a=1
rotated through 2pi radians about x axis

Answer 3

4—>1 Spiy^2dx =Spi(1+x/x)dx

piS(1/x +x/x)dx = piS(1/x +1)dx

pi((ln4+4)-(0+1))=pi(ln4+3)

Question 4

y= sqrrt(2x/x^2 +3)

b=1
a=0

rotated 2pi rotating about x axis

Answer 4

Spiy^2dx = pi S (2x/x^2 +3) dx

pi(ln4-ln3)= piln4/3

Question 5

y= 1/8x^3

b=2
a=1
volume
rotated around y axis

Answer 5

8y=x^3
x=2y^1/3
x^2=4y^2/3

12/5pi