indefinite integration

Calculus Level 3

$f(x) = \frac{9^{x}}{9^{x} + 3}$

g(x) = $\int\ f(\frac{1}{11}) + f(\frac{2}{11}) + ................ + f(\frac{10}{11})dx$

g(x) = ax + c

2 solutions

U Z
Oct 11, 2014

we can see that

f(x) + f(1-x) = 1

g(x)= $\int\ f(\frac{1}{11}) + f(\frac{10}{11}) + f(\frac{2}{11}) + f(\frac{9}{11}) ................$

g(x) = $\int\ 5$

= 5x + c

Sanjeet Raria
Oct 11, 2014

A similar problem …here I've discussed the general class of such functions.