Compute the following:
-
where
-
where
is fixed with
and,
To evaluate the integrals of these piecewise defined functions we break the integral into parts so that the intervals of integration correspond to the definition of the functions we have. (We can always split the interval of integration into pieces since the integral is additive with respect to the interval of integration by Theorem 1.17 of Apostol.)
- We split the interval
into
and
to obtain,
- We split the interval
into the two intervals
and
and compute,
sorry, what does fracc^3 means? Thanks
It’s just a LateX error. There’s a missing backslash before “frac”, so the renderer doesn’t know what to do with it. That last term should be (c^3)/(2(1 – c)).