00:01
High from the question given that consider the given graph so by using this graph we need to find for part a integral three to nine f of x d x where n is equal to three using this information we need to find left remand sum so here del x is equal to b minus minus a divided by n which is equal to 9 minus 3 divided by n is 3 so this is equal to 2 now the region here we need to find from this to this point so left rectangle rematch sum for n is equal to 3 x i is 3 5 7 since we need to subdivide the integral with the length 2.
01:15
So here f of x will be if xi is 3, then f of x is 2.
01:22
Similarly, if it is 5, then it is approximately 4 .5.
01:26
Then if it is 7, then it is approximately 6 .5.
01:34
So, integral 3 to 9 f of x, dx is equal to del x, f of x 3 plus f of x5 plus f of x7, which is equal to 2 times of 2 plus 4 .5 plus 6 .5.
02:06
Simplify it further we obtained two times of 13.
02:10
Therefore, we conclude that this will be equal to 26.
02:17
That is, the approximate value of left remand sum integral 3 to 9, f of x, d x, will be equal to 26.
02:32
Now let us move on to part b.
02:37
So for part b, we need to evaluate the integral 0 to 9 f of x, dx.
02:47
By using the value n is equal to 4, we need to find right, remand, sum.
02:56
So from the above figure, we need to evaluate the integral from 0 to 0 to 9.
03:06
By using the same procedure as we applied in part a, first we need to find del x...