Find the average value of the function on the given interval.
f(x)=x^2e^2x; [0,2]

Step-by-step explanation:

We are given that a function

We have to find the average value of function on the given interval [0,2]

Average value of function on interval [a,b] is given by

Using the formula  

By Parts integration formula

u= and v=

Apply by parts integration

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)