HOLIDAY POST NUMBER THREE

LAST DAY OF VACATION :( :( :(

Okay, more integration.

So, the sign that looks like a big S called the integral symbol and means you do the opposite of a derivative.

There are two types of integration: indefinite and definite.

Indefinite integration is when the answer is an equation.
In indefinite integration all the same properties of derivatives apply.

Definite integration is when the answer is a number.
Definite integration uses the integral [a,b].

So, integrating:

Polynomials
Sx^n dx = (x^(n+1))/(n+1) + C

Example:
Sx^3 dx = x^4/4 = 1/4 x^4 + C

For integrating trig., you basically have to know all your formulas of deriving sin, cos, etc. before you can integrate them.

Example:
S sinx dx = -cosx + C
S sec^2x dx = tanx + C
S 2cscx cotx dx = -2cscx + C

To make the integration problem you face a whole lot easier, you can rewrite the problem (if it works).

You can rewrite exponents at the bottom of a fraction to the negative form at the top.

Example:
1 / x^2 = x^-2
So when you put that into an integration problem it would be:
S 1 / x^2 = S x^-2
So then you simplify that to
x^-1 / -1
Which equals
-1/x + C

Another example:
S sinx / cos^2x dx
= S (1 / cosx)(sinx / cosx) dx
= S secx * tanx dx
= secx + C

Definite ingetration uses a and b to find the definite area under a curve/graph.

Formula for definite integration:
b S a f(x) dx = f(b) - f(a) = number

See you all tomorrow!!!