13th post

so this week we learned about indefinite integrals and definite integrals its pretty much like derivatives, so:

indefinite integrals:

an indefinite integral is just the symbol with an equation behind it. taking an integral is just like taking the derivative backwards. if you are given x^3, instead of subtracting one from the exponent, you would add and instead of multiplying the coefficient by the exponent, you would divide. and no matter what problem it is, you must mark the end of your problem with + C. the reason you do this is because c counts as any possible constant that could be there. your answer for indefinite integrals will always be an equation!
for example:
S x^2 + 4x + 9
S x^3/3 + 4x^2/2 + 9x + C

definite integrals:

a definite integral is pretty much the same except there will be two numbers found at the top and bottom of your integral symbol (the long skinny "s") and after your equation.. it will be marked with dx, but you pretty much ignore that. you treat it the same, you take the derivative backwards.. the only thing is that you pllug in your top number "b" into the derivative and your bottom number "a" into the derivative. once you do that.. you subtract f'(b) - f'(a), then you have your answer. you do not have to mark this answer with + C. your answer for definite integrals will always be a number.

reminder:

Rules for Limits:
1. if the degree of top equals thedegree of bottom, the answer is the top coefficient over bottom coefficient
2. if top degree is bigger than bottom degree, the answer is positive or negative infinity
2. if top degree is less than bottom degree, the answer is 0

related rates!!!:

The steps for related rates are:
1. Pick out all variables
2. Pick out all equations
3. Pick out what you are looking for
4. Sketch a graph and label
5. Create an equation with your variables
6. Take the derivative respecting time
7. Substitute back into the derivative
8. Solve

linearization:

The steps for solving linearization problems are:
1. Pick out the equation
2. f(x)+f`(x)dx
3. Figure out your dx
4. Figure out your x
5. Plug in everything you get


alright so im kind of understanding this indefinite and definite integrals business. im still having difficulties with linearization a little i think im getting better but i could use some examples.