Calculus! PLEASE PLEASE PLEASE I NEED HELP!!?
Water is poured into a bucket according to the rate F(t)=(t+7)/(2+t), and at the same time empties out through a hole in the bottom at the rate E(t)=(ln(t+4))/(t+2), with both F(t) and E(t) measured in pints per minute. How much water, to the nearest pint is in the bucket at time t=5 minutes.
[tex] \int\limits^5_0 {F(t)} \, dt [/tex] - [tex] \int\limits^5_0 {E(t)} \, dt [/tex] or [tex] \int\limits^5_0 {F(t)-E(t)} \, dt [/tex] so first simlify F(t)-E(t) (if you want, not necicary if use calculator) (t+7-ln(t+4))/(t+2)=F(t)-E(t)
evaluate [tex]\int\limits^5_0 \frac{t+7-ln(t+4)}{t+2} } \, dt[/tex]≈9.05584 about 9 pints
