Pumping stations deliver oil at the rate modeled by the function D, D(t)=5t/1+3t with t measure in hours and and D(t) measured in gallons per hour. How much oil will the pumping stations deliver during the 4-hour period from t = 0 to t = 4? Give 3 decimal places.

Question

anonymous · Answer

@iambatman @ganeshie8

anonymous · Answer

@nikato

anonymous · Answer

@dan815

caominhim · Answer

any interval is t2 - t1

so find D(4) - D(0)

anonymous · Answer

1.538?

anonymous · Answer

20/13-0=1.538

caominhim · Answer

well 0/0 is not 0, have you learned derivatives?

anonymous · Answer

yes, what would it be then aren't we just subtracting?

caominhim · Answer

correct, however 0/0 is indeterminate so you have to find another form of the equation. 
use l'hopital's rule

take the derivative of the top and bottom and plug in x.  do this until the answer isn't 0/0

anonymous · Answer

can you please show me the steps on doing that?

caominhim · Answer

sure let me type it up

anonymous · Answer

thank you!!!

caominhim · Answer

omg i'm so sorry this is all wrong, you were right, just subtract 0

anonymous · Answer

its okay! & thanks :)

anonymous · Answer

do you mind helping me with 3 more?

caominhim · Answer

wow nope, still wrong let me type this back up, read it wrong really sorry

anonymous · Answer

its okay :)

caominhim · Answer

D(t) is the rate at which the oil is pumped and you want the amount, that's just going to be
$$\int\limits_{0}^{4}f(x)dx$$sorry about all that

caominhim · Answer

and this time i'm positive this is the answer

anonymous · Answer

got it :) thanks

anonymous · Answer

would 0 be the answer?

anonymous · Answer

http://www.wolframalpha.com/input/?i=derivative+of+integral&f1=f(x)&f=DerivativeIntegral.integrand_f(x)&f2=x&f=DerivativeIntegral.derivativevariable%5Cu005fx&f3=x&f=DerivativeIntegral.integralvariable_x&f4=0&f=DerivativeIntegral.rangestart_0&f5=4&f=DerivativeIntegral.rangeend%5Cu005f4

anonymous · Answer

wait sorry

anonymous · Answer

http://www.wolframalpha.com/input/?i=+integral&a=*C.integral-_*Calculator.dflt-&f2=f(x)&f=Integral.integrand%5Cu005ff(x)&f3=&f=Integral.variable_&f4=0&f=Integral.rangestart%5Cu005f0&f5=4&f=Integral.rangeend%5Cu005f4 i didn't get one

caominhim · Answer

to do this by hand i'm pretty sure you need to do partial fractions, which i don't remember at all, but if you want to trust wolfram, it's not a total loss

anonymous · Answer

kk :) thanks