# I can't figure out how to do this problem.I know I have to combine 2 of the integrals somehow but I'm not sure how. Thanks for your help! "Suppose that f and h are integrable and that...

I can't figure out how to do this problem.I know I have to combine 2 of the integrals somehow but I'm not sure how. Thanks for your help!

"Suppose that f and h are integrable and that

`int_1^9f(x)dx=-1` `int_7^9f(x)dx=5` `int_7^9h(x)dx=4`

Use the rules to find: `int_1^7f(x)dx`

*print*Print*list*Cite

### 1 Answer

If `f` is integrable on segment `[a,b]` then for any `c in [a,b]` the following holds

`int_a^bf(x)dx=int_a^cf(x)dx+int_c^bf(x)dx`

Hence,

`int_1^9f(x)dx=int_1^7f(x)dx+int_7^9f(x)dx`

`-1=int_1^7f(x)dx+5`

`int_1^7f(x)dx=-6`