00:01
Where as to calculate the given integral and first we need to choose the order of integration.
00:06
In this case, in this case it doesn't really matter, so we'll choose it to be dy dx.
00:13
Then we'll get the double integral of e to the 4x plus y dy dx.
00:22
The limits of integration for y are from 1 to ln 5 and the limits of x are from 0 to ln 4.
00:32
Now we'll make a substitution u equals 4x plus y.
00:41
Here we need to recall that we are integrating with respect to y first, therefore when calculating du we will differentiate with respect to y too.
00:50
And we'll get that du equals dy.
00:53
We also need to create new limits of integration.
00:58
To get the new upper limit we need to plug in the old upper limit for y.
01:02
For y we'll get 4x plus ln 5 and for the new lower limit we'll get 4x plus 1.
01:16
And after the substitution we'll get the integral from 0 to ln 4 or the integral from 4x plus 1 to 4x plus ln 5 of e to the u du dx.
01:37
Then we'll get the integral from 0 to ln 4 of e to the u in substitution from 4x plus 1 to 4x plus ln 5 dx.
01:52
Now we'll plug in the limits...