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!

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# Which function suits this description?

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