The atmospheric pressure of the air changes with height above sea level. The rate of change of the height above sea level for a given air pressure can be measured by the differentiable function f(p), in kilometers per psi, where p is measured in psi. What are the units of int_(2)^(5)f(p)dp? kilometers psi kilometers / psi psi / kilometer kilometers //psi^(2) psi / kilometer ^(2)

Question

The atmospheric pressure of the air changes with height above sea level. The rate of change of the height above sea level for a given air pressure can be measured by the differentiable function  f(p), in kilometers per psi, where  p is measured in psi. What are the units of  int_(2)^(5)f(p)dp? kilometers psi kilometers / psi psi / kilometer kilometers  //psi^(2) psi / kilometer  ^(2)

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Function Representation: The integral of a function with respect to a variable gives the accumulation of the quantity represented by the function over the interval of integration. In this case, the function f(p) represents the rate of change of height with respect to air pressure.Integration Interval: Since f(p) is given in kilometers per psi, integrating f(p) with respect to p over the interval from 2 to 5 psi will accumulate the total change in height over that interval of air pressure.Units Calculation: The units of the integral will be the units of the function f(p) multiplied by the units of the variable of integration, p. Since f(p) has units of kilometers per psi and p has units of psi, the psi units will cancel out when multiplied.Final Result: Therefore, the units of the integral ∫_(2)^(5)f(p)dp will be in kilometers, as it represents the total change in height in kilometers over the change in air pressure from 2 to 5 psi.

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