the symbol for an integral is a long skinny capital S. there are 2 different kinds of integrals, definite and indefinite.
indefinite intergrals
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. your answer for indefinite integrals will always be an eqn.
definite intergrals
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 number
limit rule is easy. 1. if the top and bottom exponents are the same, the answer is the top coefficient over the bottom coefficient.
2. if the top exponent is bigger than the bottom exponent, the answer is infinity.
3. if the top is less than the bottom, it goes to 0.
im not too good at angles of elevation and optimization still troubles me
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 number
limit rule is easy. 1. if the top and bottom exponents are the same, the answer is the top coefficient over the bottom coefficient.
2. if the top exponent is bigger than the bottom exponent, the answer is infinity.
3. if the top is less than the bottom, it goes to 0.
im not too good at angles of elevation and optimization still troubles me
rickyyy
ReplyDeleteoptimization is easy.
primary is the one you are optimizing
other equation is secondary
solve your secondary for one variable and then plug into the primary
take the derivative
set equal to 0 and solve for variable
take that variable and plug back into secondary to get the other variable.
voila.
okay the primary is the one you are optimizing and the other equation is the your secondary. then solve for one variable and then plug into the primary then take the derivative, set equal to zero and solve for your variable. then, take that derivative and plug back into secondary to the other variable.
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