Find Definite Integral, from -2 to 4, of (5)(2^x) dx

[bjackson11]

Need a jump start on this one.

I have the problem (5)(2^x)dx The lower limit is -2 and the upper is 4. (I don't know how to put the symbols of integration in the equation) I would think that the integral would be (5x)(2^x/ln2). The back of my book has it as
5(2^x/ln2). Why do we not take the anti-derivative of the 5? Is it because the 5 is a constant?

 

[chivox]

Re: Definite Integral Question

For future reference, you have to use "TeX" which appears as a little button over the editing window:

\(\displaystyle \int_2^4 5 \cdot 2^x dx\)

This is achieved by writing

\int_2^4 5 \cdot 2^x dx

in your message, highlighting that whole thing, and clicking the "tex" button.

There's also a lesson on this board about TeX, so maybe you could look at that as well.

As for your question, let's take a simpler case to illustrate the underlying concept: what is the integral of a constant times, say, x?

\(\displaystyle \int 3 x dx = \frac{3 x^2}{2}\)

Right? That's just the constant itself times the integral of the factor with the variable in it....

 

[bjackson11]

OK thanks.....I was looking at the 5 as if it was 5 + 2^x