# Thread: Applications of Integration + SHM

1. ## 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?

2. #1: You can use shells or washers.

Shells:

$2{\pi}\int_{-1}^{4}(y+1)\sqrt{4-y}dy$

Washers:

${\pi}\int_{-\sqrt{5}}^{\sqrt{5}}(4-x^{2})^{2}-(-1)^{2}dx$

3. Shells?... Washers!?