Integration Questions (1 Viewer)

[rand_althor]

Hey, I saw I was reading through the 3U marathon and saw the following question:

How exactly do you do this? There was a solution a post or two later which split the parabola into two branches, but I don't understand that method. Can someone please explain?

Also is it possible to find the area between from to ? If so, how do you do it?

 

[Drsoccerball]

Hey, I saw I was reading through the 3U marathon and saw the following question:



How exactly do you do this? There was a solution a post or two later which split the parabola into two branches, but I don't understand that method. Can someone please explain?

Also is it possible to find the area between from to ? If so, how do you do it?

you first draw the graph and notice how there is two radiuses you have to rotate around the y axis... You cant just do an instant substitution since you'll rotate the part that you dont want around the axis therefore :








The rest should be easy for you

 

[rand_althor]

So the outer radius is the parabola from x=1 to x=2, and the inner radius is the parabola from x=0 to x=1?

Also is it possible to find the area between from to ? If so, how do you do it?

 

[Drsoccerball]

So the outer radius is the parabola from x=1 to x=2, and the inner radius is the parabola from x=0 to x=1?

The more longer method is to find the two different volumes and subtract one from the other
Its like the question asking you to find the volume bounded by the x axis of ln(x) between 2 and 3....
And the second question is exact same working out as the previous question and exact answer

 

[Drsoccerball]

The more longer method is to find the two different volumes and subtract one from the other
Its like the question asking you to find the volume bounded by the x axis of ln(x) between 2 and 3....
And the second question is exact same working out as the previous question and exact answer

Its known as dummy variable (doesn't matter what variable you have) eg:

so the second question is just a demonstration of that

 

[Ekman]

The more longer method is to find the two different volumes and subtract one from the other
Its like the question asking you to find the volume bounded by the x axis of ln(x) between 2 and 3....
And the second question is exact same working out as the previous question and exact answer

Well the method that rand_althor is mentioning is basically washer method. You are finding a bigger volume and subtracting from a smaller volume, so it would take exactly the same amount of time.

 

[Drsoccerball]

Well the method that rand_althor is mentioning is basically washer method. You are finding a bigger volume and subtracting from a smaller volume, so it would take exactly the same amount of time.

I dont think he knows washers method i mentioned inner and outer radius thats why he said it

 

[rand_althor]

I don't know what the washer method is.

Thanks for the help guys!