(a) Integrate the following function with respect to t:\

F(x)=(\\\\beta \\\\alpha ^(\\\\beta ))/(t^(\\\\beta +1)),\\\\alpha

\ where

\\\\alpha

and

\\\\beta

are constants.\ (b) Differentiate the following function with respect to

x

:\

G(x)=1-((\\\\alpha )/(x))^(\\\\beta ),\\\\alpha

\ where

\\\\alpha

and

\\\\beta

are constants, and evaluate

G(\\\\alpha )

and

G(\\\\infty )

.

4. (a) Integrate the following function with respect to t: F(x)=t+1,tx where and are constants. (b) Differentiate the following function with respect to x : G(x)=1(/x),x