Definite Intergral

**reptile7383** · December 15th 2008, 04:10 PM

$\int_{1}^{7} \frac{2^x}{x} dx$

I'm a having trouble starting this problem. Would you use integration by parts or something else?

Thanks in advance for any help

**mr fantastic** · December 15th 2008, 04:13 PM

Originally Posted by reptile7383

$\int_{1}^{7} \frac{2^x}{x} dx$

I'm a having trouble starting this problem. Would you use integration by parts or something else?

Thanks in advance for any help

Are you expected to get an exact solution? Then I have bad news: It can't be done using a finite number of elementary functions.

An approximate solution (using technology) is your only option.

**reptile7383** · December 15th 2008, 04:22 PM

The study guide says to make an estimation using 3 subintervals. I really don't recall my prof. going over anything like this so I really don't know what he wants from it.

**mr fantastic** · December 15th 2008, 04:36 PM

Originally Posted by reptile7383

The study guide says to make an estimation using 3 subintervals. I really don't recall my prof. going over anything like this so I really don't know what he wants from it.

Well it certainly helps now that you've included all of the question.

Read this:

Left and Right Rectangle Rules and Midpoint Rule

Numerical Integration

Also refer to your study guide and class notes. If you've been asked to do this then it must be there in your notes somewhere.

**reptile7383** · December 15th 2008, 04:46 PM

Sorry for not posting the whole questions. I was focused on trying to the the code for the problem correct that I forget part of the question

Anyways thanks again for your help

**Mathstud28** · December 15th 2008, 04:52 PM

Originally Posted by reptile7383

$\int_{1}^{7} \frac{2^x}{x} dx$

I'm a having trouble starting this problem. Would you use integration by parts or something else?

Thanks in advance for any help

Remember your Riemann sums? Lets use left hand.

Suppose that $f$ is Riemann integrable on $[a,b]$ then $\int_a^b f(x)dx\approx\sum_{k=1}^{n}f\left(\Lambda_k\right) \Delta x$

With $\Delta x=\frac{b-a}{n}$ and $\Lambda_k=a+\Delta x\cdot k$ . So using $n=3$ gives us

$\Delta x=\frac{7-1}{3}=2$
$\Lambda_k=1+\frac{7-1}{3}k=1+2k$
$f\left(\Lambda_k\right)=\frac{2^{1+2k}}{1+2k}=2\fr ac{4^k}{1+2k}$

So

$\begin{aligned}\int_1^7 \frac{2^x}{x}dx&\approx\sum_{k=1}^{3}2\cdot\frac{4 ^k}{2k+1}\cdot 2\\<br /> &=4\sum_{k=1}^{3}\frac{4^k}{2k+1}\\<br /> &=\frac{5744}{105}\end{aligned}$

Thread: Definite Intergral

LinkBack

Thread Tools

Display