Reflection

In calculus this week, we started learning information from chapter 4. We learned about integration and integrals.
To take a derivative you would:
F(x) = 2x^2
F’(x) = 4x
Now you are doing the opposite of taking the derivative.

For integration the symbol I’ll be using is S
Examples:
1. S(2x-3x^2)dx = S2x^2-3x^3dx
=2x^2/2 – 3x^3/x + c
= x^2 – x^3 + c this answer is called an anti-derivative
2. S1/2x^3dx = S1/2x^-3dx
= 1/2x^-2/-2 + c
= -1/4x^2 + c
3. S(t^2-cost)dt
= 1/3t^3 + sint + c

Helpful-Derivative of: sectan > sec
sec^2 > tan
csccot > csc

bSa is where it starts and stops with area.
To find the fundamental theorem of calculus:
F(b) – F(a)
a> smaller #
b> bigger #
Examples:
1. Find the area of the region bounded by the graph of y=2x^2-3x+2, the x-axis and the
vertical x=0 and x=2.
2S0 2x^2-3x+2
2[x^3/3] – 3[x^2/2] + 2x
(2/3(2)^3 – 3/2(2)^2 + 2(2)) – 2/3(0)^3 – 3/2(0)^2 + 2(0)
= 10/3
Then you would graph the equation to see what is between 2 and 0.

2. y=cosx
pi/2S0
sinx
sin(pi/2) – sin(0)
= 1