Question

Let R be the region bounded by the graphs of y=x^3 - 4x, as shown in the figure above.
a.) find the area
b.) the horizontal line y=-2 splits the region R into two parts. Write, but do not evaluate, an integral expression for the area of the part of R that is below this horizontal line.
c.) the region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a square. Find the volume of this solid.
d.) the region R models the surface of a small pond. At all points in R at a distance x from the y-axis, the depth of the water is given by h(x)=3-x. Find the vo

Answer 1

*volume of water in the pond.*

Answer 2

@agent0smith

Answer 3

Picture would probably be helpful... https://www.google.com/search?q=x%5E3+-+4x&aq=f&oq=x%5E3+-+4x&aqs=chrome.0.57&sourceid=chrome&ie=UTF-8

I don't know what limits w/o a pic.

Answer 4

Sorry I'm kinda using my iPad for this so I can't draw a picture :/ do yo u have a graphing calculator like a i3 83 plus or something?