Thread: Applications of Integration + SHM

Hi, all. Ultra stuck on a few questions, and help would be much appreciated.

- a) Show that x = Asin(3t + a), where A and a are constants, satisfies this differential equation.

My working: ---- dx/dt = 3Acos(3t + a), (d^2x)/(dt^2) = -9Asin(3t + a), therefore = -9x
Is this enough?

#1: You can use shells or washers.

Shells:



Washers:

Shells?... Washers!?

The integrals are helpful, ta!

Any hints on the others?