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I can't figure out how to do this problem.I know I have to combine 2 of the integrals...

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chrissy93b | Student, Undergraduate | (Level 1) eNoter

Posted April 8, 2013 at 5:03 PM via web

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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`

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted April 8, 2013 at 7:38 PM (Answer #1)

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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`

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