00:01
The objective of this problem is to compute the integral, integral from 0 to b x root of x square plus b square d x, where b is greater than 0.
00:16
First of all, understand that to evaluate this integral with respect to x, we are going to use the u substitution method.
00:25
So, we are going to assume that the value of x square plus b square is equal to u.
00:33
So, we need to compute the value of d u.
00:37
So, d u will be equal to 2 times x times d x.
00:44
If we differentiate b square a constant with respect to x or any other variable, we will get zero only.
00:52
So, this is the value of d u.
00:54
But what we have here is x times dx so the value of x times d x will be equal to d u divided by 2 and we shouldn't forget to find the limit of u these are the limits of x so we need to substitute x is equal to 0 and x is equal to b in this equation to find the corresponding value of u if we substitute x is equal to zero in that equation we will get u is equal to b square and similarly if we substitute x is equal to b we will get u is equal to to b square so the limit of u is nothing but b square to to b square so the given integral will be equal to integral from b square to to b square this value will become root of u and the value of x times d x will be come d u divided by 2.
01:59
So this integral will be equal to 1 by 2 times integral from b square to to b square root u d u...