Reflection

In calculus this past week we did stuff with substitution, so you need to know how to integrate and find bounds for some substitution problems. Lately we have been doing a lot of stuff with integrals, so we definitely need to know how to integrate. Here is an example of integration.

EXAMPLE:

1. Find the integral of: x^3 + 3x
When finding the integral, you have to add one to the exponent and divide that number.
x^4/4 + 3(x^2/2)
1/4x^4 + 3/2x^2 + c

2. Find the integral of: 6x
6[x^2/2]
3x^2 + c
Also when solving for integrals, do not forget to add the +c.

When finding the bounds, you set the equations in the problem equal too each other and then solve for x.

Ex :

x^2 + 2x = 3x

x^2 - x = 0

x ( x - 1 ) = 0

the bounds are x = 1, 0