CK12 Calculus - Single Variable

2. Approximatesin(0.8) to 6 decimalplaces.

Hint:considercenter

3. Approximate to 6 decimalplaces.

EvaluatingNon-ElementaryIntegrals
Thereare manysimple-lookingfunctionsthat haveno explicitformulafor their integralin the form of elemen-
tary functions.We couldwritetheir in- tegralsas TaylorSeriesin their intervalof convergence.

Example 1 Find a powerseriesrepresentationof

Solution.x-1 Since is not definedatx= 0, we applythe TaylorSeriesofexat,say,x= 1 by writingex=e.e
with a changeof variableu=x- 1.

so

whereu=x- 1

Example 2 Find the powerseriesrepresentationof

Solution.Directsubstitutionofx^2 in the MaclaurinSeriesofsin xgives

and

Exercise