## anonymous 4 years ago Integration and volume question: find the volume obtained when the shaded region is rotated through 360 degrees about the y axis.

1. anonymous

|dw:1328364703100:dw| equation of curve: y= (x+1)^0.5 equation of line: y=x+1 intersection points: (0,1) (-1,0)

2. dumbcow

$V = \pi \int\limits_{0}^{1}(y^{2}-1)^{2} - (y-1)^{2} dy$

3. anonymous

how did you get that?

4. anonymous

Revolution solid formule.

5. anonymous
6. dumbcow

outer radius is x-value of y=sqrt(x+1) --> x = y^2 -1 inner radius is x_value of y = x+1 --> x = y-1

7. dumbcow

horizontal cross-sections are rings with outer and inner radius