Calculus Integral Assignment

CalCulus- The InTegral Name_________________________________________ Mid chapter quiz

1) A grain silo has 25 cubic meters of grain in it at 3 minutes and is being filled with grain at a rate given by the

function 1

( ) cos 2

v t t t= + (in cubic.meters/min) How much grain is in the silo after 10 minutes?

2) A plane is flying due south and its velocity for given times is shown below, how far did the plane fly in the first 4 hours?

Time 0 .5 1 1.5 2 2.5 3 3.5 4 Speed (in m/s

389 375 372 370 372 381 390 400 405

3) What is the average value of 2( ) 6 14f x x x= − on the interval [1,5] ?

4) Mr. Fuller is driving west on 80 in a brand new Bentley. (Cali here I come!) He starts his journey 50 miles west of the Poconos and his velocity is given by the equation 𝑣𝑣(𝑡𝑡) = 𝑡𝑡3 − 14𝑡𝑡2 + 19𝑡𝑡 + 210 in miles/hour.

a) After 10 hours, how many miles away from where he started is he?

b) How far did he travel in 10 hours?

c) How far from the Poconos is he after 7 hours?

For Fun) What state would I, (I mean he) be in after 7 hours?