Find the volume V of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. about the x-axis y=x³, y=x, xx 0; v = Sketch the region. y -05 1.5 1.아 0.5 -0.5 x 0.5 1.0 1.5 -05 Sketch the solid, and a typical disk or washer. y 1.5 1.아 0.5 -0.5 x 0.5 1.0 1.5 -0.5 y y 1.5 1.5 1.아 0.5 -0.5 x 0.5 1.0 1.5 -0.5 1.아 0.5 -0.5 Interactive 3D Graph Help Interactive 3D Graph Help Interactive 3D Graph Help x 0.5 1.0 1.5 Interactive 3D Graph Help

For item 4-6, find the volume of solid generated byrevolving the area bounded by the given curves about theindicated axis using intergral 4. y = x2− 2x, x − axis; about the x − axis5. x + y − 5 = 0, y = 0 , x = 0; about the y − axis6. x + y − 6 = 0, y = 3 , x = 0; about the y − axis

The region bounded by the curves y = +-4>√x and the linesx = 1 and x = 4 is revolved about the y-axis to generate a solid. Find the volume of the solid.

An igloo or Eskimo hut is built in the form of a hemispherical shell with an inside diameter of 12 ft. If the igloo is constructed of snow blocks having a uniform thickness of 2 ft and weighing 40 lb per cu. ft, find the weight of the igloo, neglecting the entrance. Also, if fresh air contains 0.04 per cent carbon dioxide, find the amount of this gas in the igloo when freshly ventilated.

The volume of a right circular cone with radius r and height h is V=πr2h/3.   a. Approximate the change in the volume of the cone when the radius changes from r=5.8 to r=6.6 and the height changes from h=4.20 to h=4.18. b. Approximate the change in the volume of the cone when the radius changes from r=6.62 to r=6.55 and the height changes from h=15.0 to h=14.91. (Type an integer or decimal rounded to two decimal places as needed.)

About the right and left approximations of the area between a curve and the x-axis, it is correct to state that:    A) The right approach is the closest to the correct value  B) If we use infinite rectangles for the approximation, the sum of the areas of the rectangles will tend to the area of the region between the curve and the x-axis.    C) If the right approach tends to have infinite rectangles, then the left approach will have a different value than the right approach.  D) It is impossible to find the value of the area, as both approaches have errors.  E) Both always have the same value.

Find the area of the region bounded by the graphs of the equations.                 y = 8 − x,    x = 0,    x = 6,     y = 0

Determine the volume of the rotating object that occurs if the area of ​​the curve y1 = - x2 + 4 and the line y2 = - 2x + 4 , is rotated around the x axis, a distance of 360°?. Make the boundaries of the curve area!

1. Find the area bounded by the lines and curves  y = 4x – x² , x =1 and x = 3 2.) Find the volume of solid generated by revolving the region bounded by the lines y = 0, x = 2 and curve y = x² about the x-axis.

If x ≥ 0, find the volume of the solid obtained by rotating th reign enclose by the graphs about the line y=-8.