Hello, everyone. Tomfrom everystepcalculus.com and everystepphysics.com. I’m already at U Substitution. You scroll with these cursors, here to get to whatever in my menu that you’re interested in. You have to press alpha before you enter anything into these entry lines, here. And the problem is Alpha x times the square root of x squared plus sixteen. close off the parentheses. X times Square root of x squared plus sixteen. That’s cool. I always show you what you’ve entered. Now, how are you going to go about solving this yourself? Okay, think about it. In U Substitution notice this is a exponent of two, this is an exponent of one. okay. If the x has one less exponent than the inside of the parentheses, this is a U substitution problem. For instance, you should always in your mind to do with the derivative of something in the parentheses in Calculus. That’s one of the big deals and big tricks. So this is 2 X then. And there’s of course no derivative 16 at zero. So it’s 2x
Well here’s an X on the outside. Well, we can do something with the 2 to make
that x dx. So generally what I do what and what you should do. I say it’s okay because we’ve entered it right. You should rewrite the problem okay. So you rewrite the problem.
Square root of x squared plus 16 and you put the x dx over here so you can kinda see that you’re trying to match that somehow, okay. So then U equals x squared plus 16. Well then du equals 2x dx, okay. We take that 2 and the du divided by 2 through Algebra. And we come up with x dx. Notice that this matches the previous match of the function. so that a course you is equal to this group experts 16 So we have the Integral of u and of course the square root, in calculus you always change it to 1/2. It was a cube, it could be 1/3. If it was the 15 root, you’d be 1/15, okay. That’s Algebra 2. I mean also. So and then you have the DU divided by two so that’s a constant, you have to bring outside the integral, here. I do that for you. Here’s the 1/2 outside the integral and then we do the U to the 1/2 inside and
then integrate that part, okay. And that turns out to be this this this and the answer is 1/3, etc. So, have a good one. everystepcalculus.com