AP Calculus AB - Integrals and Differential Equations

Integrals and Differential Equations-52Q:What are the steps you should follow when trying to find integrals?

Integrals and Differential Equations-52A:The steps to integration are:
1. u-sub
2. arcs?
3. simplify

Integrals and Differential Equations-53Q:What are the steps to finding a particular solution of a differential equation?

Integrals and Differential Equations-53A:The steps to find a particular solution:
1. get y’s with dy’s and x’s with dx’s
2. integrate
3. put the +C with x’s
4. solve for y (if you e the plus C, it becomes times C) (stop here for general solutions)
5. plug in the initial condition to solve for the C
6. find the domain

Integrals and Differential Equations-54Q:How do you know that a problem is asking you to find the particular solution?

Integrals and Differential Equations-54A:A problem is asking you to find the particular solution if a differential equation is given (dy/dx=equation) and it asks for what the original equation or solution was.

What do you need to “add” to the antiderivative if there’s no “a” or “b” boundaries?

plus C!