Answer
2
Work Step by Step
In order to integrate this function, we have to use an «u» substitution.
Choose an u, derivate it:
$ u=2x-1$
$ du=2dx$
$ \dfrac{1}{2}du=dx$
Change limits:
$x_1 =1$
$u_1=2(1)-1=1$
$x_2 =5$
$u_2=2(5)-1=9$
Then substitute:
\[ = \dfrac{1}{2}\int_{1}^{9} \dfrac{du}{\sqrt{u}} =\dfrac{1}{2}\int_{1}^{9} u^{-1/2} du\]
Then integrate
\[ \bigg [ u^{1/2} \bigg ]_{1}^{9} \]
Apply calculus 2nd theorem and simplify:
\[ 9^{1/2}-1^{1/2}=3-1=2\]
