The atmospheric pressure of the air changes with height above sea level. The pressure of the air at a given height above sea level can be measured by the differentiable function f(h), in psi, where h is measured in kilometers. What are the units of int_(0)^(5)f^(')(h)dh? psi kilometers psi / kilometer kilometers / psi psi / kilometer ^(2) kilometers //psi^(2)

Question

The atmospheric pressure of the air changes with height above sea level. The pressure of the air at a given height above sea level can be measured by the differentiable function  f(h), in psi, where  h is measured in kilometers. What are the units of  int_(0)^(5)f^(')(h)dh? psi kilometers psi / kilometer kilometers / psi psi / kilometer  ^(2) kilometers  //psi^(2)

Bytelearn · Accepted Answer

Net Change Definition: The integral of a derivative represents the net change of the function over the interval. In this case, we are integrating the derivative of pressure with respect to height over a certain height interval.Derivative Units: The derivative f'(h) represents the rate of change of pressure with respect to height, so its units are psi per kilometer (psi/km).Integration Explanation: When we integrate f'(h) over an interval of h in kilometers, we are essentially summing up these small changes in pressure over the distance. The units of distance (kilometers) will cancel out the denominator of the rate of change (psi/km), leaving us with just the units of pressure.Units of Integral: Therefore, the units of the integral from 0 to 5 of f'(h)dh will be psi, since we are calculating the total change in pressure over a certain interval of height.

Full solution

More problems from Solve quadratic equations: word problems

Related topics