Post something.

So this week in Calculus we took two new AP tests which came from a Texas website...I think...

Anyway, compared to tests we have taken before, these were a bit harder I would say...

Something they really liked to do was tangent inverse and sin inverse integration. For tangent, usually

dx/(1+x^2) will integrate to tan inverse. However, they were doing things such as dx/(1+4x^2).

The trick to this is to notice that 4x^2 can be changed to (2x)^2. Now, using substitution, u = 2x and du = 2. So, accounting for the du of 2 which should be in the top, this now becomes

(1/2)arctan(2x) + C.

Also, for

dx/(sqrt(a^2 - x^2)

this will become arcsin(x/a) + C


So for instance, the integral of dx/(sqrt(4-x^2)) would be arcsin(x/2) + C

Other than that, this test focused a lot on volume.

Something that some people are still a little confused about is when revolving about the y axis.

Basically, whatever you are rotating about is what you need to have your equation in terms of...so if you are rotating about the y axis, the function would be f(y)=y^2+1, If it was rotated about the x axis, it would be sqrt(x-1) = y, These are important steps.

Also, if you change it from f(x) to f(y), and you don't have bounds, you have to set the two f(y)'s equal to each other and solve for your equations.
From here on you will just use the same steps as normal...which is on top, and if its washers, top squared minus bottom squared..

Anyway, those are still a little bit confusing to some people but we will see how it goes...

Gotta go to a birthday party...