Intergrals

[InterserveVB]

How would I go about this type of problem?

The integral of f(x) from 1 to 5 is equal to a number say -3 and the integral of f(x) from 1 to 10 is equal to say -7. They want me to find the value from 5 to 10.

 

[soroban]

Hello, InterserveVB!

\(\displaystyle \L \int^{\;\;\;\;5}_1f(x)\,dx\:=\:-3\;\) and \(\displaystyle \L \int^{\;\;\;\;10}_1 f(x)\,dx\:=\:-7\)

\(\displaystyle \text{Find: }\L\int^{\;\;\;\;10}_5f(x)\,dx\)

Think of definite integrals as areas.

      |   1       5
    - + - + - - - + -
      |   :::::::::
      |   *:::-3:::
      |    *::::::*
      |       * * 



      |   1       5 . . . .10
    - | - + - - - + - - - - +
      |   ::::::::::-7:::::::
      |   *::::::::::::::::::
      |    *::::::* *:::::::*
      |       * *      * *

Got it?

 

[InterserveVB]

I think so, is the answer -10?

 

[InterserveVB]

Do I just subtract the 1 to 5 from the 1 to 10?

 

[stapel]

Do I just subtract the 1 to 5 from the 1 to 10?

Yes.

Eliz.