00:01
Hi, now we are going to find what is the slope of the line.
00:04
Now the line is divide the region bounded by the parabola y is equal to 2x minus 5x square and the x -axis.
00:15
So first we have to draw this parabola in the graph.
00:31
Now this is our required parabola.
00:34
So the line will be passes through like this.
00:38
So first we have to find the limit for integration.
00:42
So we have to equate these two given axis.
00:48
So we get 2x minus 5x square is equal to 0.
00:54
This can be written as x into minus 5x plus 2 is equal to 0.
01:00
So from this we get x is equal to 0 and x is equal to 2 divided by 5.
01:05
Then the area of the region bounded by y is equal to 2x minus 5x square and x -axis will be integral from 0 to 2 divided by 5 2x minus 5x square into dx.
01:36
After integration and substituting the limit this will be equal to 4 divided by 75 unit square.
01:45
Now the line passes through the point 0 comma 0 and intersect the parabola at x is equal to a.
02:11
So we have the value of y will be 2a minus 5a square...