- #1
Niaboc67
- 249
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My teacher mentioned this was a very important thing to know in calculus, he didn't explain too much about it but tried to emphasize how important is it.
If $$P=\{a,x,...,x_{k-1},x_{k},...,x_{n}=b\} , P^*=\{a,x,...,x_{k-1},x^*_{k},x_{k},...,x_{n}=b\}$$
Then, $$L_{f}(P)≤L_{f}(P^*)≤U_{f}(P^*)≤U_{f}(P) $$
"So adding pts to partition to get P* raises lower sum & decreases upper sum"Any ideas guys?
Thanks
If $$P=\{a,x,...,x_{k-1},x_{k},...,x_{n}=b\} , P^*=\{a,x,...,x_{k-1},x^*_{k},x_{k},...,x_{n}=b\}$$
Then, $$L_{f}(P)≤L_{f}(P^*)≤U_{f}(P^*)≤U_{f}(P) $$
"So adding pts to partition to get P* raises lower sum & decreases upper sum"Any ideas guys?
Thanks