Thursday

August 21, 2014

August 21, 2014

Posted by **kchik** on Tuesday, December 11, 2012 at 12:54pm.

(a) Sketch the line and the curve on the same set of axes.

(b) Find the area of A.

(c) The part of A above the x-axis is rotated through 360degree about the x-axis. Find the volume of the solid generated.

(d) The surface of a swimming pool takes the shape of A where the depth of the water at any point (x,y) in A is given by (x+2). Find the volume of the water in the swimming pool.

- calculus -
**Steve**, Tuesday, December 11, 2012 at 2:34pmthe curves intersect at (1,2) and (3,0)

A = ∫[1,3] (3-x) - (x^2-5x+6) dx

= -x^3/3 + 2x^2 - 3x [1,3]

= 4/3

the parabola dips below the x-axis on the interval (2,3), so we want to rotate between the curves on [1,2] and under the line on [2,3]:

V = ∫[1,2] pi (3-x)^2 - (x^2-5x+6)^2 dx

+ ∫[2,3] pi (3-x)^2

= 12/10 pi + 1/3 pi = 23/15 pi

for the pool, multiply each strip of area by its depth:

V = ∫[1,3] (x+2)((3-x) - (x^2-5x+6)) dx

= -x^4/4 + 2/3 x^3 - 5/2 x^2 - 6x [1,3]

= 16/3

**Related Questions**

calculus - The line y+x=9 intersects the curve y=x^2-2x+3 at the points P and Q...

Calculus - This is another textbook number that doesn't have the solution and I ...

integral Calculus - The region in the x-y plane bounded by the curve y=x^2, the ...

calculus - A region is bounded in the second quadrant by the curve y = ln(1–x), ...

Calculus - 1. Find the area of the region bounded by the curves and lines y=e^x ...

Calculus - Let R be the region bounded by the curve x=9y-y^2 and the y- axis. ...

Calculus 2 - The volume of the solid generated by revolving the region about the...

Calculus - Find the volume of the solid generated by revolving the following ...

calculus - Find the volume of the solid generated by revolving the region about ...

calculus - Compute the area of the region in the fi…rst quadrant bounded on...