Wednesday

October 22, 2014

October 22, 2014

Posted by **Claire** on Thursday, May 9, 2013 at 4:59pm.

Compute the volume of the region obtained by revolving R around the y-axis

- MATH Calculus Homework -
**Steve**, Thursday, May 9, 2013 at 5:06pmwith discs (washers),

v = ∫[0,1] π (R^2-r^2) dy

where r=x and R=1

v = π∫[0,1] (1 - y^(2/3)) dy

= π (y - 3/5 y^(5/3)) [0,1]

= 2/5 π

with shells,

v = ∫[0,1] 2π rh dx

where r=x and h=y

v = 2π∫[0,1] x*x^3 dx

= 2π (1/5 x^5) [0,1]

= 2/5 π

- MATH Calculus Homework -
**Claire**, Thursday, May 9, 2013 at 5:18pmFirst off, thank you answering my question.

I just have one question. So does it matter which method we use?

I am just trying to find a better way of understanding this problem from a visual perspective.

- MATH Calculus Homework -
**Steve**, Thursday, May 9, 2013 at 5:36pmgenerally it doesn't matter. It depends on whether it is easier to express y as a function of x, or vice-versa. For example if y=e^x + 4(x^2-1) then it's pretty tough to come up with y

^{-1}

In this case, it was easy.

**Answer this Question**

**Related Questions**

calculus - The figure shows the region bounded by the x-axis and the graph of . ...

Calculus - The following are about an infinite region in the 1st quadrant ...

calculus - F(x)=e^(-3x/2) Let R be the region between the graph of f and the x-...

Calculus - The following are about an infinite region in the 1st quadrant ...

Calculus AB - Consider the region trapped between the graphs of y=9-x^2 and y=11...

Calculus AB - Consider the region trapped between the graphs of y=9-x^2 and y=11...

calculus - find the volume of the prolate spheroid (a solid of revolution in the...

calculus - 1. Let R be the region in the first quadrant enclosed by the graphs ...

calculus - Give the volume of the solid generated by revolving the region ...

MATH - Find the volumes of the solids generated by revolving the region in the ...