MATH 123 Chapter 16: MATH 123 - Chapter 16
10 Aug 2017
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Chapter 16: further techniques and applications of integration. Integration by parts is derived from the product rule for derivatives. If (cid:1873) and (cid:1874) are differentiable functions, then: We can use definite integral formulas to calculate the volume of a solid of revolution and the average value of a function on some interval. If (cid:1858)(cid:4666)(cid:1876)(cid:4667) is a nonnegative and is the region between (cid:1858)(cid:4666)(cid:1876)(cid:4667) and the (cid:1876)-axis from (cid:1876)=(cid:1853) to (cid:1876)=(cid:1854), the volume of the solid formed by rotating about the (cid:1876)-axis is given by: The average value of a function (cid:1858) on the interval [(cid:1853),(cid:1854)] is: (cid:2869)(cid:3029) (cid:3028) (cid:1858)(cid:4666)(cid:1876)(cid:4667)(cid:1856)(cid:1876) provided the indicated definite integral exists. We can also use definite integrals to study continuous money flow. value is: If (cid:1858)(cid:4666)(cid:1872)(cid:4667) is the rate of money flow, then the total money flow over the time interval from (cid:1872)=0 to (cid:1872)= is given by:
