00:02
In this problem, we are provided with the graph of y equals to square root of 1 minus x squared, which has been divided into equal intervals of width 0 .2 each.
00:20
We are asked to find out the upper sum and the lower sum.
00:30
We need to correct both to three decimal places.
00:33
So let us begin by finding out the upper sum.
00:40
The upper sum is equal to the equal width which is 0 .2 times square root of 1 minus 0 plus square root of 1 minus 0 .2 the whole squared plus square root of 1 minus 0 .4 the whole squared plus square root of 1 minus 0 .4 the whole squared plus square root of 1 minus 0 .4 the whole squared plus 1 minus 0 .6 the whole squared plus square root of 1 minus 0 .8 the whole square.
01:16
So now evaluating this we get 0 .2 times of square root of 1 plus square root of 0 .96 plus square root of 0 .84 plus square root of 0 .64 and finally square root of 0 .36.
01:45
So now evaluating all of these square roots, we get 0 .2 times of 1 plus 0 .9798 plus 0 .9165 plus 0 .8 plus 0 .6.
02:01
So further adding up all of these values, we get 0 .2 times.
02:07
4 .2963 which is approximately equal to 0 .859.
02:18
So this is the final answer for the upper sum.
02:22
Next, moving towards the lower sum...