Answer:
V(2) = 3.346
(answer choice E. )
Step-by-step explanation:
Implementing fundamental theorems of calculus we can create this
[tex]\int\limits^2_1 {ln(1+2^t)} \, dx = v(2)-v(1)[/tex]
we are looking for v(2) and we know v(1) = 2 (given in the problem)
so the equation made can be modified to the following
[tex]\int\limits^2_1 {ln(1+2^t)} \, dx = v(2)-2\\[/tex]
rewrite the integral in the first part as
[tex]\frac{Log[2^{1/2 t + 1}(2^{-1/2 t} + 2^{1/2 t})}{2\\}[/tex]
Using a partial integration you can express the integral of log(cosh(p t) in terms of the integral of t tanh(pt) and some simple shifts in the integration limits will allow you to find the analytical expression.
this can be plugged into a calculator to do
and so you will get
[tex]1.346= v(2)-2\\[/tex]
and so [tex]v(2) = 3.346[/tex]
