00:01
The objective of this problem is to sketch the region and write the equivalent double integral such that the order of integration is reversed.
00:10
We are given that the integral is from minus 2 to plus 2 and the integral from 0 to 4 minus 2x, d .y, d x.
00:23
First of all, understand that this integration means that the value of y ranges between.
00:31
0 to 4 minus 2x and the value of x ranges between minus 2 and plus 2.
00:40
So for x is equal to minus 2, if we substitute x is equal to minus 2 in this expression, we will have the value of y to be equal to 4 minus 2 times minus 2 which is equal to 8.
00:57
And if we substitute x is equal to 2 in this equation we will have y to be equal to 0 so when y is equal to 4 minus 2 x the coordinates will be minus 2 comma 8 and 2 .0 and when y is equal to 0 the coordinates will be minus 2 comma 0 and 2 .0.
01:27
Now let's plot these points and sketch the region.
01:35
Here observe that this line will be the line of y is equal to 4 minus 2x and this vertical line will be x is equal to minus 2 and so this will be the required area of integration.
01:53
So in the given options option a is the correct answer.
01:59
Now let's move on to the path b...