acceleration/velocity problem

[jeng]

How exactly can you integrate a(t) = ln (1+2^t) without integration by parts?

I have my AP exam tomorrow!!

Thanks

 

[pka]

\(\displaystyle \L
v(t) = \int {a(t)dt}\)

 

[skeeter]

got news for you ... this is a calculator driven problem.

as pka posted, the antiderivative of acceleration is velocity, but this particular problem involves a definite integral rather than a definite one ...

$\displaystyle \int_1^2 a(t) dt = v(2) - v(1)$

$\displaystyle v(1) + \int_1^2 a(t) dt = v(2)$

now ... get out your calculator and do the sum on the left side of the equation.

The AP exam does not require one to know how to integrate
$\displaystyle ln(1+2^t)$ by hand.