difficult limit: lim[t->0] (int[0,1][(bx+a(1-x))^t]dt)^(1/t)

[dts5044]

13. Find:
lim ([integral from 0 to 1] (bx + a(1-x))[sup:2yuiraxy]t[/sup:2yuiraxy] dt)[sup:2yuiraxy]1/t[/sup:2yuiraxy]
t --> 0

where the real numbers b > a > 0

I worked on this problem for a while, but the presence of both t and x confuses me. How should I do this?

 

[royhaas]

Isn't the integration with respect to x? If so, apply L'Hospital's Rule to the logarithm.