Hello, Tom of everystepcalculus.com and everystepphysics.com. A definite integral over X and Y. Let’s do it. Index 8 index to get to my menu. Scroll down to D section. Definite Integral X over XY. Double Integral. Enter the function. Alpha before you enter anything into the entry lines. This one on the internet. X times Y squared divided by parentheses, you always put parentheses in denominators. X squared plus one. I don’t know who dreams up these functions but somebody does. Remember, we’re not learning calculus for life long desires unless you’re a math major. We’re learning Calculus to pass a test. To get through Calculus. Never to touch it again. Keep that in mind, okay. Press enter here. And see if that’s what you entered. I say it is. And we’re do it over to DY, DX. And remember that D you integrate with respect to Y first when it’s DY here and DX second. And so DY is these limits of integration. And DX is these limits. So the limits given in this problem were X for 0. Alpha 0, Alpha 1. And for AY was Alpha minus 3. And Alpha 3. And here’s the Integral right here. And we’ve done the integral with respect to Y. Here’s the answer: X times Y cubed divided by 3 times x squared plus 1. And we’re going to do that over -3 and 3. So when Y equals 3, you enter these quotation marks are where you enter parentheses on your paper. Okay. Because that’s substituting Y for anything in these functions, these answers. Another one, -3 is when Y equals minus 3, these is the, you put parentheses around quotations marks. This is the answer. This is the answer for when you put three up there and you subtract the upper limit from the lower. and you get 18 X for x squared. Now we’re doing the integral of that answer over 0 in 1 limits. So we do on the integral of that which equals 9 times log of X squared plus 1. At x equals 1, this is the answer. 9 times log over 2. log 2 and x equals 0. 9 times log over zero x squared plus one which equals zero. Upper limit from the lower is this minus the 0. And so this is the answer also but when you work it out, it comes up to 6.24 square units. Pretty neat, huh? Go to my site and subscribe it you want to see more movies.