Which function's definite integral from a to b will be equal to its definite integral from b to b + (b-a)/2?(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int_{a}^{b} f(x) dx = \int_{b}^{b+\frac{b-a}{2}} f(x) dx [/tex]

[tex] \int_{a}^{b} f(x) dx = \int_{b}^{\frac{3b-a}{2}} f(x) dx [/tex]

I know that the exponential function e^x will have a definite integral for the second area that is twice as large as the first, and that the next one ((3b-a)/2 to (9b-3a)/2) will be twice as large as the second... so would this function be the exponential function divided by some function like 2^(n-1), where n is the number of the term in the sequence of definite integrals? How would I represent this function without the use of n?

Thanks for any help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Which function suits this description?

**Physics Forums | Science Articles, Homework Help, Discussion**