Find out the volume of the solid -x = (y - 2)2, Mathematics

Find out the volume of the solid obtained by rotating the region bounded by x =  (y - 2)2 and  y = x around the line y = -1.

Solution : We have to first get the intersection points there.

y =( y - 2)2

y = y 2 - 4 y + 4

0 =y 2 - 5 y + 4

0 = ( y - 4) ( y -1)

Therefore, the two curves will intersect at y = 1 & y = 4 . Following is a sketch of the bounded region and the solid.

2212_solid3.png

Following are our sketches of a typical cylinder. The sketch on the left is here to illustrates some context for the sketch on the right.

425_solid4.png

Following is the cross sectional area for this cylinder.

A ( y ) = 2 ∏ ( radius ) ( width )

=2 ∏ ( y + 1) ( y - ( y - 2)2 )

= 2 ∏ (- y3 + 4 y 2 + y - 4)

The first cylinder will cut in the solid at y = 1 and the final cylinder will cut in at y = 4 . Then the volume is

V=∫dc A(y)dy

=2 ∏∫4-y3 + 4y+ y- 4 dy

=2 ∏ (-(1/4) y4 + (4/3)y3+(1/2)y2 - 4y)|41

=(63 ∏/2)

Posted Date: 4/13/2013 6:16:49 AM | Location : United States







Related Discussions:- Find out the volume of the solid -x = (y - 2)2, Assignment Help, Ask Question on Find out the volume of the solid -x = (y - 2)2, Get Answer, Expert's Help, Find out the volume of the solid -x = (y - 2)2 Discussions

Write discussion on Find out the volume of the solid -x = (y - 2)2
Your posts are moderated
Related Questions
sir/madam, i abdulla working as a maths teacher want to join ur esteemed organisation as a tutor how can i proceed i have created an account even pls guide me, thanks abdulla

what is the lower levl of produc for MCB bank

Q. What is Stem-and-Leaf Plots? Ans. A stem-and-leaf plot is a table that provides a quick way to arrange a set of data and view its shape, or distribution. Each data val

I need to make an assignment on this topic what should i write in it

can you offer help with an entry level marketing class and with developing charts and tables for the final marketing plan?

Tangents with Polar Coordinates Here we now require to discuss some calculus topics in terms of polar coordinates. We will begin with finding tangent lines to polar curves.

How does finding the unit rate help make smart decisions?

what is the nearest ten thousand of 92,892?

As noted, Euler's method is little used in practice, as there are much better ways of solving initial value problems. By better, we mean, "able to achieve a result of the same prec

Explain The Decimal System in detail? A decimal, such as 1.23, is made up of two parts: a whole number and a decimal fraction. In 1.23, the whole number is 1 and the decimal fr