00:01
We are given with an equation integral from 0 to 1000 a to the power of x d x minus integral from a to thousand a to the power of x d x is equal to 10 .40 and we are asked to find the value of a which satisfies this equation.
00:25
To do that first of all understand that integral of a to the power of a with respect to x is nothing but 8 to the power of x divided by lan 8 plus c where c is the integration constant here as we have limits we have to substitute them instead of adding the integration constant c so the given integration will be equal to 8 to the power of x divided by lam 8, the limits 0 to 1000 minus the second integration will be the same one, 8 to the power of x divided by lan 8, the limits from 8 to 1000.
01:14
And this will be equal to 10 .40.
01:19
So if we substitute the limits, we will get 8 to the power of thousand.
01:24
First we have to substitute the upper limit.
01:27
So instead of x we have to substitute thousand divided by lan 8 minus the lower limit 0.
01:34
So 8 to the power of 0.
01:37
Anything power 0 is 1.
01:38
So 8 to the power of 0 is 1.
01:41
1 divided by lan 8 minus the upper limit in this term...