Amount of dye is mg and dye concentration is , .

The cardiac output is .

Where is the amount of dye and the integral can be approximated from the concentration readings at any time during the interval .

Consider .

Find the integral using by parts.

Integration by parts: .

Here and .

Differentiate on each side.

.

Find by integrating .

Substitute corresponding values in the by parts formula.

.

.

.

The cardiac output is .

The cardiac output is .