1. ## partial fraction integration, please check my working out

 . What is the exact value of ? Give your answer as a fraction or whole number. I split the fraction, into two fractions, using partial fractions method, to get img.top {vertical-align:15%;} $\int^2_0 \frac{2}{x+4} -\frac{2}{x+5}$ = img.top {vertical-align:15%;} $ln(x+4) - ln(x+5)$ img.top {vertical-align:15%;} $ln\frac{x+4}{x+5}$ x=2 x=0 img.top {vertical-align:15%;} $ln\frac{6}{7} - ln\frac{4}{5}$ img.top {vertical-align:15%;} $ln \frac{30}{28} = 0.06899$ is the the value of k?

2. ## Re: partial fraction integration, please check my working out

You made one error in your integration, you neglected the 2 in the numerator of your integrands, which just means you need to square 30/28 = 15/14 to get the value of k.

3. ## Re: partial fraction integration, please check my working out

Originally Posted by MarkFL2
You made one error in your integration, you neglected the 2 in the numerator of your integrands, which just means you need to square 30/28 = 15/14 to get the value of k.
oh yes thank you, so the value of k is 1.071?

4. ## Re: partial fraction integration, please check my working out

No, you wind up with:

$2\ln\left(\frac{15}{14} \right)=\ln(k)$

$\ln\left(\left(\frac{15}{14} \right)^2 \right)=\ln(k)$

And so:

$k=\left(\frac{15}{14} \right)^2=\frac{225}{196}$