00:01
All right, we're going to do u substitution for this problem, the integral from 0 to 1, of the square root of 5x plus 4 dx.
00:11
So i tell my students to look for a grouping symbol.
00:15
The square root is a group.
00:18
So i'm going to do everything that's under the square root.
00:21
And then du, the derivative of that would be 5dx.
00:25
And in my experience, my students need to rewrite this as dividing the 5 over.
00:30
The reason why that's helpful, i think, is because then students can say, oh, okay, well, this is equal to the integral.
00:37
I'll mess with the bounds here shortly.
00:39
I can replace 5x plus 4 with u.
00:42
I'm going to rewrite to the one -half power.
00:44
And then i can replace dx with one -fifth, du.
00:51
And so, again, my bounds need to change.
00:53
So when i plug in 0 for x, 5 times 0 is 0, plus 4 is 4.
00:57
And then when i plug in one, five times one is five plus four is nine...