00:01
In this problem, it is given that f -dash is equal to under root 1 plus x q.
00:06
And also f of 1 is given as 0 .5.
00:09
Now using the fundamental theorem of calculus, we will get integral a to b, this is f -dash -of -x into d -x, is equals to f of b minus f of a.
00:22
Now here we choose a is equal to 1 and b is equals to 4.
00:28
Now, after substituting this, we will get integral 1 to 4 f dash of x into dx is equals to f of 4 minus f of 1.
00:42
Therefore, here, f of 4 minus f of 1 value is given as 0 to 0 .5, which is is equals to integral 1 to 4, f dash of x is given as under root 1 plus x cube into d x.
00:59
Therefore, f of 4 minus 0 .5 is equal to integral 1 to integral 1 to 4 under root 1 plus x cube value is 12 .871...