week 13

ok, so it's week 13 already and progress reports are about to come out for the 2nd nine weeks. school year is flying by!
this week we went over limits because we had a quiz on wednesday, it was scheduled for tuesday but b rob was absent. towards the end of the week, we learned something new! integrals!
the symbol for an integral is a long skinny capital S. there are 2 different kinds of integrals, definite and indefinite.
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. it will be counted completely wrong if you dont! 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!
for example:
3
S x^2 dx
0

= x^3/3 ..... (3)^3/3 - (0)^3/3 ...... = 9-0
= 9


just remember that these problems do get harder. some involve functions like sine and cosine. same rules apply though, just remember your derivative rules for those types of functions.
i need help with 35 and 37 on the back page...(293) of the homework, its pictures! what do i do?