00:01
In this question we are asked to find the volume of the solid obtained by rotating the region enclosed by the graphs of y equals to 15 minus x, y equals to 3x minus 5 and x equals to 0 about the y axis.
00:12
So let's start to solve this problem.
00:14
Here to solve this problem first we draw the region bounded by these curves.
00:18
Here this is the x -y plane.
00:21
Now in this equation if we put x equals to 0 then we obtain y equals to 15.
00:27
And when we put y equals to 0 then we obtain x equals to 15 comma 0 hence here this is the line y equals to 15 minus x now next here if we put x equal to 0 then we obtain y equals to negative 5 negative 5 and here when we put y equals to 0 then we obtain x equals to 5 power 3 so here this is the line y equals to 3x minus 5 now next, this is the line, x equals to 0.
01:32
Now next to find this point, we put y equals to 15 minus x here.
01:37
15 minus x is equal to 3x minus 5, 20 is equal to 4x, x is equal to 5.
01:48
4x equals to 5 we obtain y is equal to 10.
01:53
That means this point is 5 .10...