- #1
stunner5000pt
- 1,461
- 2
Let f (x) = 1 if 2<=x<4
2 if x =4
-3, if 4<x<=7
Prove that this function is integrable on [2,7], state its value and prove that it is what you say it is.
Obviously integral of f from [2,7] is -7. but its proof and the integrability have me and my friends snagged.
Suggestions anyone?
SO far we have the idea that we have to prove that U(f,P) - L(f,P) , Epsilon
We computed that U(f,P) - L(f,P) =5 (Tj - Tj-1) where Tj and Tj-1 is the subinterval in which Tj-1<2<Tj. However we are stuck from here.
My notation is from a book called Calculus by Spivak. Basically U(f,P) is the upper sum and L(f,P) is th lwoer sum for a partition P of the interval. P = {A=T0,T1,T2,...,TJ-1,TJ,...TN=B}and A and B are the endpoints of hte interval.
2 if x =4
-3, if 4<x<=7
Prove that this function is integrable on [2,7], state its value and prove that it is what you say it is.
Obviously integral of f from [2,7] is -7. but its proof and the integrability have me and my friends snagged.
Suggestions anyone?
SO far we have the idea that we have to prove that U(f,P) - L(f,P) , Epsilon
We computed that U(f,P) - L(f,P) =5 (Tj - Tj-1) where Tj and Tj-1 is the subinterval in which Tj-1<2<Tj. However we are stuck from here.
My notation is from a book called Calculus by Spivak. Basically U(f,P) is the upper sum and L(f,P) is th lwoer sum for a partition P of the interval. P = {A=T0,T1,T2,...,TJ-1,TJ,...TN=B}and A and B are the endpoints of hte interval.