4.3. The Area Problem http://www.ck12.org
Review Questions
In problems #1–2 , find the summations.
1.∑^10 i= 1 i( 2 i− 3 )
2.∑ni= 1 ( 3 −i)( 2 +i)In problems #3–5, findS(P)andT(P)under the partitionP.
- f(x) = 1 −x^2 ,P={ 0 ,^12 , 1 ,^32 , 2 }
- f(x) = 2 x^2 ,P={− 1 ,−^12 , 0 ,^12 , 1 }
- f(x) =^1 x,P={− 4 ,− 3 ,− 2 ,− 1 }
In problems #6–8, find the area under the curve using the limit definition of area.
- f(x) = 3 x+5 fromx=2 tox= 6.
- f(x) =x^2 fromx=1 tox= 3.
- f(x) =^1 xfromx=1 tox= 4.
In problems #9–10, state whether the function is integrable in the given interval. Give a reason for your answer.
- f(x) =|x− 2 |on the interval[ 1 , 4 ]
- f(x) =
{
1 ifxis rational
− 1 ifxis irrationalon the interval[^0 ,^1 ]