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Hello everyone.
00:02
In this question we have been given a function f which is defined in the interval of 0 to 6 and there is another function z of x which is defined as integration of f of t d t from 1 to x and the function f is defined by the graph which is shown here and we have to find the value of z of 4.
00:31
So to solve this problem, we can write g of 4 is equal to integration of f of t d t from 1 to 4.
00:45
So we can write this g of 4 is equal to function f of t from 1 to 2 d t plus integration of f of t d t from 2 to 4 since because the after 0 .2, the graph or the function is changing.
01:05
So we will consider this as equation 1.
01:08
Now we will take this part as 1 and this part as 2.
01:14
So for first part that is in the limit of 1 to 2.
01:21
So for the limit of 1 to 2, so for the limit of 1 to 2, f of t is a line joining the 2 points.
01:35
That is 1 minus 2 and 2 0.
01:40
So the equation of this line, equation of line joining 1 minus 2 and 2 0 is x minus 1 divided by 2 minus 1 equal to y minus minus 2 divided by 0 minus 2.
02:07
So if we solve this, we will get x minus 1 divided by 1 equal to y plus 2 divided by 2...