Question

the integral [1, 500] (13^x -11^x)dx + the integral [2, 500] (11^x -13^x)dx=..... please help and show all steps!

Answer 1

seems like you can simplify this by using a bit of algebra and a definite integral theorem (maybe its a theorem, im not quite sure):

\[ \int_{a}^{b} f(x) dx = \int_{a}^{c} f(x) dx + \int_{c}^{b} f(x) dx \]

the second integral, if we factored out a -1 and took it to the outside, it would be the same function as the first. maybe that'd help fix it up a bit