Sunday

November 23, 2014

November 23, 2014

Posted by **naseba** on Thursday, March 29, 2012 at 8:40am.

a. Find the area of the region R.

b. Find the value of h such that the vertical line x = h divides the region R into two regions of equal area.

c. Find the volume of the solid generated when R is revolved about the x -axis.

d. The vertical line x = k divides the region R into two regions such that when these two regions are revolved around the x – axis, they generate solids with equal volumes. Find the value of k.

- calc -
**Reiny**, Thursday, March 29, 2012 at 9:02ama)

Area of region from x=0 to x=4

= ∫x^(1/2) dx from x=0 to 4

= [ (2/3)x^(3/2) ] from x = 0 to 4

= (2/3)(4^(3/2)

= (2/3)(8) = 16/3

b)

so we want

∫x^(1/2) dx from x = 0 to h to have a value of 8/3

(2/3)h^(3/2) = 8/3

h^(3/2) = (8/3)(3/2) = 4

h = 4^(2/3) = 16^(1/3) or cuberoot(16) or appr 2.52

c) this next part can be done in the same way

first let's find the volume from x-0 to 4

V = π∫ x dx from 0 to 4

= [(1/2)πx^2 ] from 0 to 4

= (1/2)π(16) = 8π

d) set the integral equal to 4π and solve for k

I am sure you can handle the rest

- calc -
**naseba**, Thursday, March 29, 2012 at 9:07amthanks

**Answer this Question**

**Related Questions**

calculus - let R be the region bounded by the x-axis, the graph of y=sqrt(x+1), ...

Calculus - Let f be the function given by f(x)=(x^3)/4 - (x^2)/3 - x/2 + 3cosx. ...

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

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

calculus - A region is bounded by the function y=2x^2+3 and the x-axis over the ...

Calculus - This problem set is ridiculously hard. I know how to find the volume ...

math - let R be the region bounded by the graphs of y = sin(pie times x) and y...

calculus - let R be the region bounded by the graphs of y = sin(pie times x) and...

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

Calculus - Find the area of the region bounded by the line y=3x and y= x^3 + 2x^...