00:01
The question is to evaluate the integral, integral 0 to log 5, integral 1 to log 4, e raise to x plus 4 y, d, d x.
00:16
Now, to evaluate this integral, first write it as integral 0 to log 5, integral 1 to log 4, e raised to x times e raised to 4 y, d, y, dx by using the properties of exponents.
00:33
Now, e raise to x is a constant with respect to y.
00:37
Therefore, this can be written as integral 0 to log 5, e raise to x times integral 1 to log 4, e raised to 4 y, d ,y, dx.
00:50
Now, evaluate the inner integral, that is, integral 0 ,000 ,000.
00:55
To log 5 erase to x times evaluating the integral with respect to y we have it as erase to 4 y divided by 4 and the limits of integration is from 1 to log 4 d x now this is integral 0 to log 5 erase to x by 4 times erase to 4 y and the limits of integration is from 1 to log 4 t x.
01:26
Now applying the limits this is integral 0 to log 5, e raised to x by 4 times e raise to 4 log 4 minus e raise to 4 t x.
01:41
Now by property of logarithms we can simplify this is integral 0 to log 5, e raise to x by 4 times, e raise to log 4, erase to log 4.
01:54
4 minus e raised to 4 d x now by using the property of exponents this is integral 0 to log 5 e raised to x by 4 times 4 minus e raised to 4 d x now this is 256 minus e raised to 4 d x...