compute.
LessonSummary
- We usedRiemannSumsto approximateareasundercurves.
- We evaluateddefiniteintegralsas limitsof RiemannSums.
ReviewQuestions
In problems#1–7, use RiemannSumsto approximatethe areasunderthe curves.
- Consider from to Use RiemannSumswith four subintervalsof equal
lengths.Choosethe midpointsof eachsubintervalas the samplepoints. - Repeatproblem#1 usinggeometryto calculatethe exactareaof the region underthe graphof
from to (Hint:Sketcha graphof the regionand see if you can computeits
area usingarea measurementformulasfrom geometry.) - Repeatproblem#1 usingthe definitionof the definiteintegralto calculatethe exactarea of the region
underthe graphof from to - from to Use RiemannSumswith five subintervalsof equallengths.
Choosethe left endpointof eachsubintervalas the samplepoints. - Repeatproblem#4 usingthe definitionof the definiteintergalto calculatethe exactarea of the region
underthe graphof from to - Consider Computethe RiemannSum of on undereachof the followingsituations.
In eachcase,use the right endpointas the samplepoints.
a. Two sub-intervalsof equallength.
b. Five sub-intervalsof equallength.
c. Ten sub-intervalsof equallength.
d. Basedon your answersabove,try to guessthe exactarea underthe graphof on
- Considerf(x) = e^x. Computethe RiemannSumof f on [0, 1] undereachof the followingsituations.In
eachcase,use the right endpointas the samplepoints.
a. Two sub-intervalsof equallength.
b. Five sub-intervalsof equallength.
c. Ten sub-intervalsof equallength.
d. Basedon your answersabove,try to guessthe exactarea underthe graphof on
- Find the net area underthe graphof ; to (Hint:Sketchthe graphand
checkfor symmetry.)