Word Problems - Calc AB Review related

Snow falls intermittently accumulating on the ground at a rate (inches/hour) given by the equation $f(t) = t^2sin{t^3} + 2.5$ where t is the number of hours that storm is overhead. To the nearest inch, how much snow will accumulate in the first two hours of the storm?

Do I just plug in 2 hours into the equation to get 6.46 in? It seems to simple to work like that though.

The temperature of a city for the 24 hour period starting at 12 noon is given by equation $T(t) = 19 + 15sin\frac{x\pi}{12}$ where t is the number of hours after 12 noon. Find the average temperature of the city to the nearest integer from 12 noon until 6 am the next morning.
So is t = 18? and I just use the formula $favg = \int_{12}^{18}\frac{T(t)}{18 - 12}$ ?

Quote:

Snow falls intermittently accumulating on the ground at a rate (inches/hour) given by the equation http://www.mathhelpforum.com/math-he...7394726e-1.gif where t is the number of hours that storm is overhead. To the nearest inch, how much snow will accumulate in the first two hours of the storm?

Do I just plug in 2 hours into the equation to get 6.46 in?

no ... f(t) is a rate that snow accumulates on the ground.

amount of snow that will accumulate in the first two hrs is $\int_0^2 f(t) \, dt$

Quote:

... where t is the number of hours after 12 noon. Find the average temperature of the city to the nearest integer from 12 noon until 6 am the next morning.

from noon (t=0) to 6AM (t=18)

$T_{avg} = \frac{1}{18-0} \int_0^{18} T(t) \, dt$

oh. I see . thanks!