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Sarah O.

Calculus 1 / AB

1 month, 3 weeks ago

I'M not sure exactly where you need help. If you just need setting it up- or maybe you can set up these problems, but you don't know how to evaluate, but basically what you're looking at when you're looking at this picture of x, plus 3 from negative 1 to 2 point. So they give you the visual from negative 1 to 2 and you're revolving around that x axis that you want to have the integral b from negative 1 to 2 of pi. And then you also want to make sure that you do the washer method, because you have this blank space. That'S what i tell my students. If you have blank splace, then you have to do the washing method where it's something squared minus another thing squared in terms of x. So in this problem, with your upper function being x, plus 3 and your lower function being y equals 1, and you know, depending on how you're expected to do this, you might need to foil that out, first or whatever verbage. Your teacher wants you to use 3 times. 3 is 9, but then you have to subtract of 1, so you're actually looking at 8 and then at some point, i'm gonna guess: you're going to use a calculator 1 third x cubed because you add 1 to the exponent divided by your new exponent and then Do this from negative 1 to 2 point, but i'm going to use a calculator because there's a lot of problems for me to do so. I'M hitting math 9 for the integral from negative 1 to 2 of your function, i'm actually just going to type. It is x, plus 3 squared minus 1 squared in terms of x, as i typed that in i got exactly 36 and don't forget about that pie. That'S in front so looking at the next 1 very similar, except this time, just looking at the picture because they shift the graph up 1. But now you don't have any blank space. So when you set this up, it's just going to be the disc method. So it's only 1 function squared when you revolve it around the x axis and so your function being the square root of x, plus 1 is squared and then the balance they give. You are from 1 to 4 and again i'm just going to go to a calculator nature. If so, i'm hitting math 9 point. I'M not sure if this is what you need help with by typing in the square root of x plus 1. I did something wrong closed, my parenthesis, squared d, i'm struggling to right right now there we go and as a fraction i got an answer of 196 with a pi in there and it's that very first option, because you don't have to put the pie in the Numerator, you can put it right here. Okay m on to the next 1 might need to go a little bit faster here this time it may seem different, but it's really not because they give you that square root of y and yeah they they do. Give you the right function, because it's looks like y equals x squared, but if you were to square root, both sides- that is the correct thing so in terms of y, were revolving this from 0 to 4. So this problem be the integral from 0 to 4. Of the square root of y squared, because there's no blank space in here, don't forget about your pi in front in terms of y now. This is actually a very duable problem in your head, because the square in the square would cancel. You add 1 to the exponent and divide by your new exponent, and doing this from 0 to 4 is pretty straight forward because you just do 4 square to 16, half of which is 8 and plugging in 0 will not change anything. So you have no need for a calculator on that 1 and then the last 1 is also a washer method, similar to number 8, because you're going from 1 to 4. So the function looks something like this, so the integral from 1 to 4, the upper function being 2 y. That needs to be squared minus the lower function of x equals 1 point. So again, you can probably do this now, i'm garry to square each piece. So that's 4 add 1 to the exponents divided by your new exponent and then 1 squared is 1. So it's just gonna be y and we're doing this from 1 to 4 and again because i sometimes i make mistakes, i'm going to go to a calculation and just type it in so math 9 from 1 to 42 y squared minus 1 squared is still 1 And go ahead and put in my variable and i got exactly 81 pi- let's see if that's an option and it's the last 1 there. So there you go.

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