During a rainfall, the depth of water in a rain gauge increases at a rate modeled by R (t) = 0.5 + t cos(pi*t^3/ 80) where t is the time in hours since the start of the rainfall and R (t) is measured in centimeters per hour. How much did the depth of water in the rain gauge increase from t = 0 to t = 3 hours?
Step-by-step explanation:
During a rainfall, the depth of water in a rain gauge increases at a rate modeled by R (t) = 0.5 + t cos(pi*t^3/ 80) where t is the time in hours since the start of the rainfall and R (t) is measured in centimeters per hour. How much did the depth of water in the rain gauge increase from t = 0 to t = 3 hours?