1. ## [SOLVED] definite integral

Hey,
This is actually a high school maths question but we're doing calculus so...?

okay, well this is what my maths question says:

From other sources, find the integral function of the function you were given and hence find the definite integral of your function between x=2 and x=5.

My function is 4^x and we are able to just do this with solvers on the internet, or finding methods on the internet, so I'm fine with that. I'm just unsure about exactly what the question wants.

Do I find the integral function of 4^x and then find the definite integral of that or do I just find the definite integral of 4^x straight out?

Any answer would be greatly appreciated

Thanks so much,

Anna

2. Originally Posted by ajay91
Hey,
This is actually a high school maths question but we're doing calculus so...?

okay, well this is what my maths question says:

From other sources, find the integral function of the function you were given and hence find the definite integral of your function between x=2 and x=5.

My function is 4^x and we are able to just do this with solvers on the internet, or finding methods on the internet, so I'm fine with that. I'm just unsure about exactly what the question wants.

Do I find the integral function of 4^x and then find the definite integral of that or do I just find the definite integral of 4^x straight out?

Any answer would be greatly appreciated

Thanks so much,

Anna
you want $\displaystyle \int_2^54^x~dx = \frac {4^x}{\ln 4} \bigg|_2^5 = \frac {4^5}{\ln 4} - \frac {4^2}{\ln 4} = \frac {1008}{\ln 4}$ .........this is by the fundamental theorem of calculus

so what did we learn here?

$\displaystyle \int a^x~dx = \frac {a^x}{\ln a} + C$ for $\displaystyle a> 1$

and the fundamental theorem of calculus. which in short says, if $\displaystyle F(x)$ is the anti-derivative of $\displaystyle f(x)$, then $\displaystyle \int_a^bf(x)~dx = F(b) - F(a)$ (this of course assumes $\displaystyle f$ is integrable and all that jazz)

3. $\displaystyle \int^{5}_{2} 4^x~dx$

First integrate the function $\displaystyle 4^x$, then apply the integration bounds. This is the easiest way to deal with it.

4. Yay!

Thank you so much! We've only just started work on these sorts of things in the past few days so I'm just beginning to understand where to apply what we've learnt in class!